Singular perturbation problems have been applied in various areas of mechanics, acoustics, optics, engineering and others. A class of two-dimensional parabolic singular perturbation problem with source terms is considered. The numerical scheme of the problem on spatial moving meshes is constructed by means of coordinate transformation and finite volume method. The mesh iteration method and updating method of solution on moving mesh are given, and an adaptive moving mesh algorithm with local refinement is proposed. The numerical results show that, compared with the solution on uniform mesh, the adaptive moving mesh method can reflect the local characteristics of the solution better and has better solution accuracy.