Officials said the calves - two males and a female - were filmed in Ujung Kulon park on the island of Java, between the months of April and July.
They added that the calves were born to different mothers and "looked healthy". Just one calf was spotted in 2014.
The discovery of the calves raises the number of Javan rhinos from 57 to 60 - all of them live in Ujung Kulon.
"This is wonderful news," Widodo Ramono, head of conservation group the Indonesian Rhino Foundation, told AFP news agency. "Now we just need to ensure their protection."
The Javan rhino, native to jungles across South East Asia, was once the most widespread of Asian rhinoceroses.
But it can now be found only in Ujung Kulon park.
Record numbers of the species were hunted for their horns, prized for their use in traditional Asian medicine in countries such as China and Vietnam.
Three critically endangered Javan rhinoceros calves have been caught on camera in an Indonesian national park.