In this paper, we consider a railway crew scheduling problem. In order to solve it, a mathematical programming method has been used. This method enumerates railway crew pairings, and solves a set covering problem. However, since the general mathematical programming approach requires much computational time, it is difficult to find a good schedule in an acceptable computational time for a large-scale problem. In order to reduce the computational time, we propose some heuristics for enumerating railway crew pairings and solving a set covering problem efficiently. Numerical results using a large-scale actual data show efficiencies of the proposed method.