Like Don said, it is a rimmed cartridge (that's what the "R" in the designation means), but it is definitely centerfire not rimfire. It is somewhat archaic in that respect, rimmed centerfire rifle cartridges having fallen out of favor in modern times. You can forgive it somewhat, having been designed in the nineteenth century and being a contemporary of the 30-40 Krag-Jorgensen.
It is, however, a cartridge with a lot of life left in it. I believe the 7.62x54R is still in active duty with the Russian military for one of their LMGs. Quality surplus ammo is readily available, as well as non-corrosive new production.
The rifles are a hoot to shoot, and are a great deal at the price. I have two, and even use one as my brush hunting gun. It's a great rifle for starting the milsurp addiction.