To improve the performance of pipelined data processing on computational grids, the method combining simulated annealing with a set of heuristic algorithms is presented to optimize grid scheduling. Pipelined data processing is divided into multiple subapplications, and every sub-application is supposed moldable. Thus, sub-applications should be assigned onto their appropriate grid nodes, while parallel degrees should be determined reasonably. On one grid node, subapplications are supposed to spatially share processor resources, and a set of heuristic algorithms is presented to optimize parallel degrees for different performance parameters respectively, based on which simulated annealing is simplified for optimizing sub-application assignments. Experiments show that the throughput or latency of pipelined data processing can be efficiently improved by the optimization of grid scheduling.