PGQ, a novel hybrid computational intelligence approach, in which Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and quantum computation are integrated, is proposed to solve the Vehicle Routing Problem (VRP). In PSO, a quantum approach called QUP is proposed to update the particles. GA operators are employed to improve population quality. The simulation results indicate that the PGQ algorithm is very effective and is better than simple PSO and GA as well as PSO and GA mixed algorithm.