Abstract: Task scheduling plays an important role in grid system and has a notable impact on the overall performance. Scheduling problems, as a class of NP (non-deterministic polynomial) problems can get a near optimal solution by classical scheduling approaches in most cases. Although the existing methods of task scheduling based on GA(genetic algorithms) can give better solutions to task scheduling than classical approaches, most of them are used for single task or multiple tasks which are independent on each other. An improved GA is thus proposed for task scheduling on computational grid by combining theoretical analysis with simulation results. What tasks the genetic algorithm deal with may involve many subtasks with contextual constraints and every subtask may require several kinds of resources. A comparison test showed that the genetic algorithm proposed is better than conventional HEFT and DLS algorithms during task scheduling on computational grid.