We propose a direct numerical method for calculating the statistics for the numbers of transitions in stochastic processes, without having to resort to Monte Carlo calculations. The method is based on a generating function method, and arbitrary moments of the probability distribution of the number of transitions are in principle calculated by solving numerically a system of coupled differential equations. As an example, a two-state model with a time-dependent transition matrix is considered and the first, second and third moments of the current are calculated. This calculation scheme is applicable for any stochastic process with a finite state space, and it would be helpful for studying current statistics for nonequilibrium systems.