Both reliability and transmission congestion should be considered when a wind farm is connected to a power system. Nevertheless, wind-farm capacity credit (CC) is defined currently considering reliability only. In this work, we proposed a wind-farm CC definition based on transmission congestion, built a CC model taking into account the random failures of power system components (generating units, transmission lines and transformers) using Monte Carlo technique, and proposed a solution algorithm of CC model using the bisection method. We also proposed wind power congestion indices to describe the contribution of a wind farm incorporated into a power system to alleviating transmission congestion. The case studies on a modified IEEE-RTS indicate that the proposed method is effective and feasible. The results show that for a power system, alleviation of transmission congestion is related to the wind-farm location, the combination of CC and wind power congestion indices can evaluate the effectiveness and economical efficiency of a wind farm in alleviating transmission congestion.