In this paper, an efficient metaheuristic technique is proposed for solving the static transmission expansion planning problem. This technique is known as the social spider algorithm. A suitable methodology for handling the problem constraints is also proposed. In the proposed methodology, a DC power flow sub-problem is solved for each network resulting from adding a potential solution developed by the social spider algorithm to the base network. The proposed algorithm and the accompanying constraints handling methodology have been tested through solving the transmission expansion planning problem of three benchmark systems having 6-buses, 46 buses, and 87 buses. Excellent performance and new solutions are demonstrated in the results section. The new solutions achieve a remarkable reduction in the total investment cost.