In this paper, we propose a new fixed-lag maximum likelihood smoother with a finite impulse response (FIR) structure for discrete-time state-space models. This smoother is called a maximum likelihood FIR smoother (MLFS). The MLFS is linear with the most recent finite outputs and does not require a prior initial state information on a receding horizon. It is shown that the proposed MLFS possesses the unbiasedness property and the deadbeat property. Simulation study illustrates that the proposed MLFS is more robust against uncertainties and faster in convergence than the conventional fixed-lag Kalman smoother.