To promote the rapidity and equity(fairness) in emergency rescue, a cumulative multi-depot vehicle routing problem(Cum-MDVRP) model with the objective of minimizing the cumulative waiting time in all affected areas is built. Because of the NP-hard nature of this problem, a multi-start variable neighborhood descent algorithm is developed to solve it efficiently. In each iteration, multi-start methods produce a randomly initial feasible solution by an improved Split algorithm combined with a feasibility repairing procedure, and then this solution is further improved by a variable neighborhood descent algorithm. Results of computational tests on some extended benchmark instances show the effectiveness of the proposed model and the good performance of the developed algorithm.