Task scheduling is one of the core steps to effectively exploit the capabilities of resources in the Grid. The task scheduling problem is an NP-complete problem. This paper studied on the task scheduling problem in grid environment and proposed a task scheduling mechanism, which expressed each possible task scheduling scheme as a task-resource assignment graph (T-RAG) and thus mapped the task scheduling problem into a graph optimal selection problem. Moreover, in order to find the optimal solution quickly and accurately, a task scheduling algorithm based on particle swarm optimization (PSO) was proposed. This algorithm regards the longest path of the task-resource assignment graph as fitness value and encodes every task-resource assignment as a particle. Finally, the experimentation shows that the approach proposed in this paper is effective to solve task scheduling problem.