The location-routing problem (LRP) is an important logistics problem in emergency management. Considering the risk of the extended traveling time, the risk of road connectivity, the road complexity and the demand uncertainty of relief supplies, a multi-objective optimization model based on the stochastic chance constrained programming was proposed to minimize the total transportation time and the total system cost. Then, an improved genetic algorithm (GA) with penalty function was presented to solve the optimization problem. The results of numerical examples show that the optimization model and the improved GA algorithm proposed in this paper are feasible and effective.