This paper analyzes the effects of labor union in the steady state of an overlapping generation economy when a union and a firm determine wage and employment through an efficient contract. We find that when the wage set in the bargaining is the same as the competitive level, the steady state equilibrium through the efficient contract is the same as the steady state of competitive equilibrium. We also find that an increase in the bargaining power of the union improves the welfare of the representative generation in the new steady state with a sacrifice of the current old generation. Moreover, the command optimum maximizing the welfare of the representative generation in the steady state can be achieved with the efficient contract when the bargaining power of the union is maximal so that profit of the firm becomes zero.