Power system restructuring and deregulation introduces new functions, the so-called open access to transmission network, for transmission system providers. Transmission system operators are dealing with facilitating more room for electric power transfer. The transmission expansion problem (TEP) is a crucial issue, especially as it can help competition under a new scheme of power system reform. There is a very limited capability in controlling this natural tendency of power flows, while transmission expansion is a major task to meet the growth of demand. There has been some research in this field, however, in this paper a hybridization of a meta heuristic technique associated with a conventional method is employed. Real genetic algorithm and goal attainment are combined in order to develop a constrained multi-objective optimization for TEP. By considering the load shedding of demand as well as capital cost of installation (CCI) for new transmission lines, a cost function is proposed in this paper. Case studies and results analysis on “Garver System” and IEEE 24-bus test system show the effectiveness of the proposed methodology.