The main object of this note is to prove that a filtered ringA is quasi-Frobenius, if its associated graded ring E ~ (A) is quasi-Frobenius (Theorem 1). In w 1, we discuss some generalities on quasi-Frobenius rings. In w 2, given a filtered ring A such that F~A=A for some n, we construct an injective, filtered Amodule F* such that E ~ (F*) is E ~ (A)-injeetive and a monomorphism ~: A ~ F* such that r for all i. We then prove Theorem1 using the results obtained in w 1. Unless stated otherwise the modules considered in this note are left modules. The author wishes to express her sincere thanks to Professor R. Sridharan for his valuable guidance during the preparation of this paper.