A computational recursive least-squares method is proposed of identifying the parameters of parabolic distributed parameter systems with noise-contaminated outputs. The identification algorithm of the spatially varying parameter µ(z1, z2) in the two-dimensional diffusion equation X1 = (µXz1)z1 + (µXz2)z2 + U based on measurements of X at all nodes of the spatial grid is considered. The finite-difference and finite-element methods to approximate the infinite-dimensional problem to a finite-dimensional one have been used. Finally, two examples are given to demonstrate the effectiveness of the present approach.