Abstract-Nowadays, multi-processor systems are being used extensively in parallel computing. The effective scheduling system for implementing parallel programs to achieve high performance is crucial. The timing should be done in such a way that the total execution time of the program with according to time and tasks to be minimize communication between processors. This is a NP-Hard problem which tasks graph scheduling approaches based on deterministic methods are not effective in this context while the use of evolutionary computing and genetic algorithms to solve this problem effectively are mainly. In this paper, a new genetic algorithm is proposed for the problem of scheduling tasks graph which is able to spend less time to get. This algorithm is based on a new approach to minimize the length of the critical path and the cost of communication between processors. In this paper, we calculate the number of descendants for each node in which tries to minimize the total execution time of the program.