In the presence of distributed generation (DG), it is important to assure a fast and reliable protection system for the distribution network to avoid unintentional DG disconnection during fault conditions. In this paper, dual setting directional over-current relays are proposed for protecting meshed distribution systems with DG. Dual setting relays are equipped with two inverse time-current characteristics whose settings will depend on the fault direction. The protection coordination problem for the dual setting directional relay is formulated as a nonlinear programming problem where the objective is to minimize the overall time of operation of relays during primary and backup operation. The proposed protection coordination scheme using dual setting relays is compared against the conventional approach, which relies on the conventional one setting directional relay. The proposed scheme is applied to the power distribution network of the IEEE 30-bus system equipped with synchronous and inverter-based DG. The results show that the proposed protection coordination scheme with dual setting relay can significantly reduce the overall relay operating time, making it an attractive option for distribution systems with DG