Electric power transmission utilities try to maximize profit by reducing electricity supply costs and operation costs while maintaining their reliability. Developing maintenance strategies is one of the effective ways to achieve these profitable goals. The reliability-centered maintenance approach is a key method in providing optimal maintenance strategies. It considers the tradeoffs between the upfront maintenance costs and the potential costs of reliability losses. Since a transmission system is a group of different kinds of equipment and the reliability of the electric facilities varies with time, an equipment state model using a modified semi-Markov chain is proposed. In addition, a genetic algorithm is used to find the optimal maintenance strategies from a large class of possible maintenance scenarios. These optimal maintenance strategies have been tested on an IEEE 9-bus system and an IEEE 118-bus system; the results show that the proposed method minimizes the total expected costs