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In this paper, an efficient optimization technique, called improved moth-flame optimization (IMFO) is proposed to improve the performance of conventional Moth-flame optimization (MFO). Then, both of MFO and IMFO are applied to solve the coordination problem of standard and non-standard directional overcurrent relays (DOCRs). In the proposed IMFO, the leadership hierarchy of grey wolf optimizer is used to improve the performance of conventional MFO with the aim of finding the best optimum solution. The major goal for optimal coordination of DOCRs is to minimize the total operation time for all primary relays as well as satisfy the selectivity criteria between relay pairs without any violation in the operating constraints. The performance and feasibility of proposed IMFO are investigated using three different networks (8-bus network, 9-bus network, and 15-bus). The proposed IMFO is compared with conventional MFO and other well-known optimization techniques. The results show the effectiveness of the proposed IMFO in solving both standard and non-standard DOCRs coordination problems without any violation between primary and backup relays. In addition, the results show the power of proposed IMFO in finding the best optimal relay settings and minimizing the total operating time of relays which its reduction ratio reaches more than 28% with respect to the conventional MFO. Furthermore, the reduction in the total operating time of primary relays reaches more than 50 % with the usage of the non-standard relay curve. INDEX TERMS Direction overcurrent relays, optimal coordination, improved moth-flame optimization, standard and non-standard relay curves, coordination time interval.