A parallel memetic algorithm for the NP-hard vehicle routing problem with time windows (VRPTW) is proposed. The algorithm consists of components which are executed as parallel processes. A process runs either a heuristic algorithm or a hybrid of a genetic algorithm and some local refinement procedures. In order to improve the results, processes co-operate periodically using a novel randomized scheme. During each phase of co-operation processes exploit their best solutions found so far. The purpose of the work is to devise the parallel memetic algorithm which determines the VRPTW solutions of the highest possible quality. The experiments on Gehring and Homberger's (GH) benchmarking tests show that the algorithm achieves very good results. By making use of it the best-known solutions to 171 out of 300 GH tests were improved.