Scheduling problems of grid research area are paid moreand more attention recently. In this paper, a grid Scheduling modelbased on prediction of task completion time (SPCT) is proposed. ThroughUsing Least Squares Discrete Curve Fitting, SPCT dynamicallyestablishes the regression function of Completion time of task (CTT)according to the historical record first. Predicted completion time ofeach coming task is calculated for each candidate node with theregression function secondly. And then, the node with the least valuewill be allocated to run the task. The SPCT is used to input datasensitive applications and implemented in one real-world gridenvironment, Bioinformatics Grid Platform. Experimental result showsthat the SPCT could reduce the average CTT of tasks by 19%.