The band played at the Calcutta School of Music, the Kolkata Centre for Creativity (KCC) and the consulate's National Day Reception between October 11 and 13, according to the organisers.
The consulate said the visit was meant to promote an exchange between contemporary American and Kolkata culture.
The eight-member band played rock, pop and jazz, including songs by Dolly Parton, Taylor Swift and Bruno Mars.
Its members are Katie Grace Stephenson, John Parris, Tinki Yu, Seth Burkhar, Adam Byars, Marcelo Carrion, Andrew Delnagro and Joshua Haney, all U.S. Navy music professionals.
The Orient Express (US Navy Band) performs at KCC, celebrating 250 years of independence.
Stephenson, the group's singer, led much of the show at KCC by involving the audience in the singing.
Students from schools and colleges across the city attended, along with working professionals and older couples, the organisers said.
The band regularly tours the region, using music to promote friendship, goodwill and people-to-people engagement, according to the organisers.
"It is absolutely very important for different cultures to interact," said John Parris, the band's bass player.
Parris said music is understood across cultures, whatever a listener's background.
He described the crowd at KCC as "amazing" and said the audience in Kolkata had been very accommodating.