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The cloud computing is the development of distributed computing, parallel computing and grid computing, or defined as the commercial implementation of these computer science concepts. One of the fundamental issues in this environment is related to task scheduling. Cloud task scheduling is an NP-hard optimization problem, and many meta-heuristic algorithms have been proposed to solve it. A good task scheduler should adapt its scheduling strategy to the changing environment and the types of tasks. A Genetic Algorithm (GA) for job scheduling has been proposed and produced good results. The main disadvantage of GA is time consuming problem. In this paper, the Improved GA (IGA) with good initial solution was proposed to reduce the GA execution time.