In this paper, we present a new genetic algorithm for Project Time-Cost Trade-off (TCTO) Scheduling problem. In the proposed GA, the selection of genes for mutation is adopted to be based on chromosome value, as solution convergence rate is high. This paper also offers a new multi attribute fitness function for the problem. This function can vary by DM preferences (time or cost). The algorithm is described and evaluated systematically. The computational outcomes validate the effectiveness of the suggested approach.