Currently the research on the Quality of Service (QoS) composition in ASKALON grid workflow management system is still rare,a computational method of activities' QoS of grid workflow is proposed based on abstract grid workflow language(AGWL) model Existing grid workflow scheduling algorithms commonly suffer by one or several of the following drawbacks monotonous expressing structure not enough consideration of multidimentional QoS parameters and single objective optimal scheduling. A scheduling algorithm of multiobjective optimal grid workflow scheduling with QoS constraints based on multiobjective particle swarm optimization(MOPSO) algorithm is proposed. compared with a grid workflow scheduling algorithm based on NSGA-II algorithm, the experimental results show the validity of algorithm.