Roads in the affected areas are usually damaged during big natural disasters, and it results in blocked road, reduced road capacity, lower vehicle speed and severe restrictions for travelling. Besides, vehicles are donated temporarily by numerous groups and various in their performance. This paper takes the above problems caused by road damage into consideration, and the vehicle route decision are made. Then a multiple vehicles type with different load capacity and travelling performance is considered, and the suitable vehicle type is selected for each route in order to confirm that the vehicles can pass though the assigned route safely. A mixed integer linear model is proposed for the decisions, with the aim of minimizing deliver time for relief goods as well as minimizing the number of vehicles used in the relief, and an algorithm based on Label Setting Algorithm is designed to solve the problem. Finally, a 15-node network example is adopted to numerically verify the proposed models, and the selection truck-load transportation and less-than-truck-load transportation is discussed.