We study the PBW filtration on the highest weight representations V (λ) of sp2n. This filtration is induced by the standard degree filtration on U(n-). We give a description of the associated graded S(n-)-module grV(λ) in terms of generators and relations. We also construct a basis of grV(λ). As an application we derive a graded combinatorial formula for the character of V(λ) and obtain a new class of bases of the modules V(λ).