This paper is concerned with the recursive secure filtering problem for a class of state-saturated systems suffering from false data injection (FDI) attacks. The considered system is subject to both additive and multiplicative noises modeled by several uncorrelated random sequences with known statistics. This paper aims to design a recursive filter so that, in the presence of state saturation and FDI attacks, an upper bound is derived and then minimized for the filtering error variance. Sufficient conditions are presented to ensure the existence of an upper bound on the filtering error variance based on the inductive method and stochastic analysis techniques. The filter gain is also designed to minimize the upper bound at each time step in the trace sense. Furthermore, how the FDI attacks affect the filtering performance is examined. Finally, a simulation example is given to show the effectiveness of the proposed filtering scheme.