In Grid Computing the number of resources and tasks is usually very large, which makes the scheduling task very complex optimization problem. Genetic algorithms (GAs) have been broadly used to solve these NP-complete problems efficiently. On the other hand, the Standard Genetic algorithm (SGA) is too slow when used in a realistic scheduling due to its time-consuming iteration. This paper proposes a new Rank-based Roulette Wheel Selection Genetic Algorithm (RRWSGA) for scheduling independent tasks in the grid environment, which increases the performance and the quality of schedule with a limited number of iterations, RRWSGA improves the reliability in the selection process while matching an acceptable output. A fast reduction of makespan making the RRWSGA of practical concern for grid environment. The results are encouraging, and can be used for real-world scheduling problems.