A new recursive approach for solving the 1D and 2D inverse Laplace transform problem of rational transfer functions via block-pulse functions is presented. It is shown that the piecewise constant approximations can be calculated recursively from a corresponding difference equation. This approach is thus straightforward, rather simple and suitable for computer programming. Additionally, the calculation size is small. These advantages are valuable, especially when the number of subintervals for block-pulse functions has to be large in order to obtain a satisfactory result, as shown by illustrative examples. By a parallel derivation, similar to the 1D and 2D cases, this approach is also easy to extend to multidimensional problems.