The concept of grid computing emerged with the appearance of high-speed network. Effective grid worker (i.e., computing resource) selection mechanism is important to achieve reliable grid computing system since each worker participate in grid computing is heterogeneous. In this paper, we suggest a credible worker selection mechanism that maximizes grid computing performance by allocating appropriate tasks to each grid worker. Diverse workers can be used efficiently by grid applications through the ranking process of worker's credibility. Initially, the rank of each grid worker's credibility is decided considering static information only such as CPU speed, RAM size, storage capacity and network bandwidth. And then, the rank is refined by using dynamic information such as failure rate, turn around time provided after the task is completed, and correctness of the return value. In the experiments, we find that the proposed mechanism provides improved grid computing performance with high credibility.