A vehicle routing problem with multiple demands is investigated, where each type of demand needs a special type of vehicles to provide service and the service order of one customer's multiple demands is fixed. Considering the constraints of time windows, the service order of multiple demands, the interval between different service, the capacity and total running time of each vehicle, a mix integer programming model is formulated to minimize the total costs of all vehicles. A joint optimal genetic algorithm is developed for solving the model. The effectiveness of the algorithm is verified by simulations on instances with two types of demands derived from the VRP benchmarks. This paper not only extends the classical single-demand vehicle routing problem to the multiple demands case, but also formulates a mathematical model of the multiple demands vehicle routing problem with constraints and designs an effective algorithm for solving the model, which provides a decision basis for solving practical problems.