In this paper, an iterative finite impulse response (FIR) filter is proposed for discrete time-varying state-space models, with the purpose of a new initialization strategy for the iterative FIR structure as well as consideration of possible unexpected state dynamics in a finite horizon. A compensation variable that satisfies the Gaussian property is introduced into the state equation, and its probability density function (pdf) is estimated analytically together with the pdf of state variable using the variational Bayesian inference technique. Different from the existing methods, the proposed filter exploits the FIR structure from the perspective of pdf propagation, which provides a new efficient way to use the iterative FIR filtering structure without any particular initialization scheme. Moreover, the effects of uncertainties (caused by initialization and/or possible un-modeled state dynamics) on the filtering output are loosened adaptively. Two examples of applications demonstrate that the proposed algorithm can not only provide optimal estimates when the model used perfectly matches the measurements, but can also exhibit better robustness than the Kalman filter, optimal FIR filter, maximum likelihood FIR filter, and some commonly used robust and/or adaptive Kalman filters when the underlying process suffers from unpredicted uncertainties.