Fast and reliable service restoration strategy is necessary to restore as many out-of-service loads as possible in a short time. In this paper, a mixed-integer second-order cone programming formulation is proposed for service restoration of a distribution network with distributed generations (DGs). This formulation relaxes the original non-convex power flow equations into a conic quadratic format. The employment of conic relaxation is of great importance because it ensures the quality of the obtained solution. The service restoration is formulated as a multi-objective optimization problem considering the minimization of de-energized loads and total number of switching operations. Moreover, PQ and PV model of DGs are considered in this formulation. The proposed method is tested on the 33-bus system and the Taiwan Power Company 84-bus system to show its effectiveness.