In this paper, a stochastic multi-depot multi-objective vehicle routing problem (VRP) is studied. Based on observations in real-world problems, we develop an aspect of the problem, such as stochastic availability of routes. To solve the problem in this situation, a two-objective mathematical model is developed, in which the related objective functions are: (1) minimizing transportation costs and (2) maximizing probability of delivery to customers. The second objective function, which is nonlinear, has performed to a linear function. Since this problem is NP-hard, to solve it we propose simulated annealing (SA) that is a well-known meta-heuristic algorithm. To show the performance of this algorithm, we compare the related results in terms of run-time and objective function values with the lower bound and Lingo 8 software for different sizes of the given problem.