The programme is funded by the United States and has been so successful the Micronesian republic has withdrawn from the global Covid-19 vaccine facility Covax, aimed at providing equitable access among low and middle income countries.
Covax, which is funded through wealthy governments and donor organisations, had committed 24,000 doses of the AstraZeneca vaccine to help the Marshall Islands achieve 20 percent coverage by year's end.
Deliveries were slated to begin next month.
However, the Marshall Islands Secretary of Health Jack Niedenthal said the US started supplying the Moderna vaccine in December.
"Next month we're scheduled to get 11,000 more vaccines," said Niedenthal.
"We've already got 21,000 vaccines and this is a population of about 56,000 people, and roughly half of those may be eligible."
With the overall backing by the US, the Covax facility was no longer necessary for the country, said Niedenthal, and it could now focus on other countries with greater need.
Initially front-line workers and the elderly were targeted but the jab was soon rolled out to anyone older than 18 as health workers went door-to-door.
The two dose Moderna vaccine suits small island tropical states better than the Covax options, added Niedenthal.
"The only two vaccines that they offer are Pfizer, which has an extremely rigorous and demanding cold-chain for the vaccine to be stored. Once you open it you have 10 days to use the vaccine."
The other, the AstraZeneca shot, is not yet approved by the US Food and Drug Administration (FDA).
The programme roll-out is reaching 300 to 500 people, six days a week, which means they're well in excess of the Covax facility's target, said Niedenthal.
"For our adult population here we're probably over 30 percent at this point, already, and I'm saying that the Covax programme hopes that by the end of 2021 they can have 20 percent."
The Marshall Islands Red Cross has been administering the vaccine programme.
Its Secretary General, Ainrik George, said the focus had been on the two main population centres of Ebeye and Majuro which were also international entry points.
Progress had been steady despite some reluctance, he said.
"People still hesitate to take it. They have a lot of questions. They hesitate to take it because of what other people were saying about it but, it's coming gradually and moving forward."
Having community leaders on side has really helped, George added.
"It's good to go out to the community, involving their stakeholders, traditional leaders, community leaders, church leaders and get everybody on board before it's rolled out."
It's a strategy other Pacific countries can use to battle misinformation about the virus and the vaccine.
The Secretary of Health said getting influential people behind the roll-out of their vaccine programme helped give confidence to community.
Their campaign launch received a high media profile, said Niedenthal, as it went beyond the Minister of Health, Bruce Bilimon and Chief Justice, Carl Ingram.
"We had a traditional leader, like a king - it was Kotak Loeak. And we had a religious leader, Reverend Johnny. And the speaker of the Nitijela also, the parliament, was part of that roll-out."
The Marshall Islands Red Cross is using its expertise in medical logistics, and of data capture to ensure it's known who and who isn't vaccinated.
One of those who's been administering the jab is Red Cross volunteer Silia Peter who's among those who have already received both doses.
"We've taken the vaccine. Here are some of the side effects that we encounter. And we reassure them that it's better to take the vaccine as of right now, before the actual coronavirus comes to our island."
While side-effects can include fatigue, headache, muscle and joint pain, and chills, they usually last a couple of days and many people don't get any.
They are often stronger following the second shot at 28 days.
Peters, who'd previously suffered a lung infection, said her reaction was quite extreme.
"Some of the symptoms I had during my second dose, I felt like I was having pneumonia all over again."
However, the Health Secretary said reactions should not deter people from being immunised.
"The day after my second dose I was very lethargic and I had a 101 fever, and I had chills. But the next day it was like it didn't even happen and that's normal for that vaccine," said Niedenthal.
"But there are other people, a lot of friends of mine and a couple of other doctors, they had zero reaction so it all depends on the person."
Niedenthal said the best protection for Pacific people is to be vaccinated and armed with correct information from trustworthy sources like health professionals and government agencies.