This paper investigates the [GRAPHICS] filtering problem for stochastic systems driven by Poisson processes. By utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator, this paper transforms the expectation of stochastic integral with respect to the Poisson process into the expectation of Lebesgue integral. Then, based on this, this paper designs an [GRAPHICS] filter such that the filtering error system is mean-square asymptotically stable and satisfies a prescribed [GRAPHICS] performance level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.