A feedforward neural network (FNN) implementation of a finite-memory smoother (FMS) is proposed. For a linear time-invariant dynamic system with measurement and process white noise, a single-layer FNN with delayed inputs is found to possess the same structure as the FMS designed by the least-squares method. The FNN-based FMS features definite speed advantages over conventional approaches and intrinsically finite process memory. Due to its parallel structure and absence of state vector integration, the FNN suffices for real-time applications. A numerical example illustrates the design procedure