This paper is concerned with the evaluation of the diffusion coefficient based on the measurement obtained at the boundary by using a numerical approach. We consider the problem of recovering the diffusion coefficient of a rod that is a function of space. The approach is based on finite-difference method and the least-squares scheme. At the beginning of the algorithm, the finite-difference method is used to discretize the problem domain. The present approach is to rearrange the matrix forms of the differential governing equations and estimate unknown diffusion coefficient. The least-squares method is adopted to find the solution. This solution is unstable, hence the problem is ill-posed. This instability is overcome using the Tikhonov regularization method with the gcv criterion for the choice of the regularization parameter. The stability and accuracy of the scheme presented is evaluated by comparison with the Singular Value Decomposition method (SVD). Results show that a good estimation on the diffusion coefficient can be obtained within a couple of minutes CPU time at pentium IV-2.4 GHz PC.