With the integration of distributed generation (DG) to meshed distribution systems, the operating time of the protective system becomes a major concern in order to avoid nuisance DG tripping. This paper proposes a new time-current-voltage tripping characteristic for directional overcurrent relays (DOCRs) that can achieve a higher possible reduction of overall relays operating time in meshed distribution networks. The proposed tripping characteristic is described in detail. Moreover, the protection coordination problem is formulated as a constrained nonlinear programming problem to determine the optimal relay settings. The proposed characteristic is tested on the power distribution system of the IEEE 14 bus and IEEE 30 bus with inverter-based and synchronous-based DG units. The outcome of this study reveals that the new tripping characteristic for DOCRs achieves notable reduction in total relays' operating time over the conventional characteristic.