A general scheduling framework (GSF) for independent tasks in computational Grid is proposed in this paper, which modeled by Petri net and located on the layer of Grid scheduler. Furthermore, a new mapping algorithm aimed at time and cost is designed on the basis of this framework. The algorithm uses weighted average fuzzy applicability to express the matching degree between available machines and independent tasks. Some existent heuristic algorithms are tested in GSF, and the results of simulation and comparison not only show good flexibility and adaptability of GSF, but also prove that, given a certain aim, the new algorithm can consider the factors of time and cost as a whole and its performance is higher than those mentioned algorithms.