In this paper, we address a single machine non-preemptive n-job scheduling problem to minimize the sum of earliness and tardiness with different release times and due dates. To solve the problem, we propose a genetic algorithm with new crossover and mutation operators to find the job sequencing. For the proposed genetic algorithm, the optimal pair of crossover and mutation rates is investigated. To illustrate the suitability of genetic algorithm, solutions of genetic algorithm are compared with solutions of exhaustive enumeration method in small size problems and tabu search method in large size problems. Computational results demonstrate that the proposed genetic algorithm provides the near-optimal job sequencing in the real world problem.