Grid computing is the technology used in building Internet-wide computing environment and integrating distributed and heterogeneous resources. However, in Grid environment, job scheduling is confronted with a great challenge. This paper focuses on lightweight jobs scheduling in Grid Computing. An Adaptive Fine-grained Job Scheduling (AFJS) algorithm is proposed. Compared with other fine-grained job scheduling algorithms based on grouping, AFJS can outperform them according to the experimental results. And some other related problems are also illustrated.