This paper focus on the probability-constrained filtering problem for a class of time-varying systems with successive packet dropouts and multiplicative noises. The purpose of this paper is to design a time-varying filter guaranteeing the probabilities of the estimation error are larger than a prescribed constant. Additionally the given ellipsoidal set is minimized at each time point. To achieve the probabilistic constraint objective, the probabilistic constraint is replaced by a multi-dimensional Chebyshev bound. By using a stochastic analysis method, sufficient conditions in terms of recursive matrix inequalities are established for the existence of the probability constrained filter. Then a algorithm is proposed to obtain the optimal filterand minimize the ellipsoid. Finally, a simulation example is proposed to illustrate the effectiveness and applicability of the proposed scheme.