In this paper, we propose an algorithm for numerical solving an inverse non-linear diffusion problem. The algorithm is based on the linearized nonlinear terms by Taylor’s series expansion, removed the time-dependent terms by Laplace transform, finite difference technique used for discretize problem. In additional, the least-squares method is adopted to find the solution. This solution is unstable, hence the problem is ill-posed. To regularize the resultant ill-conditioned linear system of equations, we apply the Tikhonov regularization method to obtain the stable numerical approxima- tion to the solution. To show the efficiency and accuracy of the present method a test problem will be studied.