Electric vehicles (EVs) are widely applied in logistics companies’ urban logistics distribution, as fuel prices increase and environmental awareness grows. This study introduces an EV charging station (CS) location-routing problem with time windows and resource sharing (EVCS-LRPTWRS). Resource sharing, among multiple depots within multiple service periods is proposed to adjust the transportation resource configuration for a sustainable logistics development. Solving the EVCS-LRPTWRS involves a periodic CS location selection and a multi-depot multi-period EV routing optimization. A bi-objective nonlinear programming model is proposed to formulate the EVCS-LRPTWRS with a minimum total operating cost and number of EVs. A hybrid algorithm combining the Gaussian mixture clustering algorithm (GMCA) with the improved nondominated sorting genetic algorithm-II (INSGA-II) is designed to address the EVCS-LRPTWRS. The GMCA is employed to assign customers to appropriate depots in various service periods in order to reduce the computational complexity. The INSGA-II is adopted to obtain the Pareto optimal solutions by using the CS insertion operation to select CS locations and integrating the elite retention mechanism to ensure a stable and excellent performance. The superiority of the hybrid algorithm is proven by comparison with the other three algorithms (i.e., multi-objective genetic algorithm, multi-objective particle swarm optimization, and multi-objective ant colony optimization). An empirical study of the EVCS-LRPTWRS in Chongqing City, China is conducted. Then, four types of service period divisions and three scenarios of resource sharing modes are further analyzed and discussed. The empirical results demonstrate the validity and practicability of the proposed solution method in realizing a sustainable operation in EV distribution networks.