A production distribution problem (PDP) with the third party logistics (3PL) is discussed in the present paper. Then, a PDP model is built as an extended type of vehicle routing problem (VRP), which is a classical model in logistics. The novel model can be transformed into the combination of generalized travelling salesman problem (GTSP) and TSP with constraints. Some characters about the existing solutions of PDP are discussed. As a result, a genetic algorithm for PDP is proposed. Finally the result of numerical simulation shows the feasibility and effectiveness of the new model.