Grid environment emphasis resources sharing and cooperation, that brings great not only advantages but also task scheduling problems. By harmonizing and distributing the grid resources efficiently, an advanced task scheduling strategy can reduce total run time and total expense greatly and bring an optimal performance. So task scheduling under grid environments is one of the key research fields of grid systems.At present, a number of grid tasks scheduling algorithms, such as genetic algorithm(GA), ant algorithm(AA), simulated annealing algorithm and sufferage algorithm etc, have advantages and disadvantages obviously, which can notfinish optimizing the task scheduling by itself and a strategy that combines GA and AA is not brought forward.The research thought of this thesis is modified GA and AA in order to utilize them into the task scheduling of Grid environment, making the following contribution on some related reputation problems by means of theoretical analysis and simulation experiment:●The problems of grid task scheduling are analyzed through summarizing research content and significance of grid task scheduling and research actuality;●According to the research of heuristic algorithms, a dynamic combination of genetic algorithm and ant algorithm is proposed, which has both the advantages of GA and AA. And considering the task scheduling request of grid computing environment, design a new grid task scheduling strategy based on the algorithm;●Presenting the load balance factor in the algorithm, so the balance of system is increased;●The development approach of scheduling simulation based on GridSim is presented and the simulation platform of the DCG3A is set up.●Doing a prototype experiment of the algorithms on the simulation platform and experimental results show their feasibility and superiority;