Abstract We investigate in this paper a Cauchy problem for the time-fractional diffusion equation (TFDE). Based on the idea of kernel-based approximation, we construct an efficient numerical scheme for obtaining the solution of a Cauchy problem of TFDE. The use of M -Wright functions as the kernel functions for the approximation space allows us to express the solution in terms of M -Wright functions, whose numerical evaluation can be accurately achieved by applying the inverse Laplace transform technique. To handle the ill-posedness of the resultant coefficient matrix due to the noisy Cauchy data, we adapt the standard Tikhonov regularization technique with the L -curve method for obtaining the optimal regularization parameter to give a stable numerical reconstruction of the solution. Numerical results indicate the efficiency and effectiveness of the proposed scheme.