In this paper presents an algorithm for directional over-current relay coordination based on linear programming. The relays are configured by adjusting time dial setting (TDS) of function properly in normal and fault conditions. The TDS adjustment is performed by using linear programming. For test, 6-bus and 9-bus test power systems are situated. Furthermore, there are also identified primary relay and backup relay pairs when fault occurred. Performance above that can solve the problems; adjust TDS of each relay and determine the minimum time relay coordination. The results illustrated that linear programming is simple and can be used for solving optimal coordination of directional over-current relays.