This paper is concerned with the filter implementation for a linear stochastic distributed-parameter system with a moving boundary. In the system considered here, it is assumed that the states of the system are expressed by partial differential equations, and the location of the moving boundary is expressed by an ordinary differential equation. The eigenfunction expansion method to decrease computation volume and to stabilize numerical computation for the filter implementation is introduced as follows; firstly, the estimates and their covariances are approximately expressed as a finite sum of eigenfunction series, and secondly ordinary differential equations with respect to Fourier coefficients of eigenfunctions are derived. The simulation study compares the practical applicability of the proposed method with the finite difference scheme.