In a statement last week, the museum said that it was reviewing its structure and had "opened discussions with its team offering voluntary redundancies and consultations".
A spokeswoman said that it would lose the equivalent of three full time jobs out of 34.
In 2014-15 the museum had an income of £2.27m and spent £2.56m, according to the Charities Commission website. It has run a deficit for the past five years.
Richard Doughty, the director of the museum, said: "Despite record breaking visitor numbers this year and the strongest financial performance ever, we still carry a financial deficit.
"We are determined to make the museum sustainable for the long term and although change is always unsettling, this is an opportune time to restructure and put in place a plan to reduce shortfalls."
Doughty added that the museum would be appointing a head of commerce to "lead the commercial team into a more confident future".
Richard Doughty told Museums Journal that while the museum was currently enjoying a successful year, it needed to make a 21% cut in its operational budget in order to balance its finances.
“We are facing a huge deficit on our operation for next year and we’ve been trying for several months to find ways to address that,” he said. “This isn’t a knee-jerk reaction”.
The museum has run a deficit since it opened but is expecting to make a “very small surplus” in 2015-16, said Doughty. This is due to the success of Viking Voyagers, a two-year exhibition showing items loaned from the British Museum, the National Museum of Denmark and other museums, but Doughty does not expect this to continue into the next financial year.
“Viking Voyagers has helped us to cross the line in a healthy position. The difficulty is that as soon as you move into the second year of an exhibition, numbers start to fall away,” he said.
Doughty said the museum was planning to review its pricing strategy and the new head of commerce would focus on improving the museum’s catering and retail performance and look at other ways of generating income.
He said that during the restructure the museum would “do its utmost” to protect its “core competencies” including the knowledge and skills needed to care for its boat collection, as well as its education services and work with communities.
“We want to reach out to our communities, we want to work with school groups, we want to protect the expertise and knowledge that we have around our core collection. Those are things we will want to protect as long as we can do so,” he said.
Despite its problems, Doughty believed that NMMC was in a healthier position than many local authority-run museums, saying “We’re used to standing on our own two feet and we are pretty agile.”