The purpose of the article is to study an f-cosymplectic manifold M admitting Ricci solitons. Here we consider mainly two classes of Ricci solitons on f-cosymplectic manifolds. One is the class of contact Ricci solitons. The other is the class of gradient Ricci solitons, for which we give the local classifications of M. We also give some properties of f-cosymplectic manifolds.