Grid is widely distributed and promising technology that enables the integrated and heterogeneous resource sharing for solving computationally challenging scientific engineering problems. In a distributed grid environment, allocating the tasks to the available computing resources proves complex and it is an NP-Complete problem as resources are geo-graphically distributed. In this paper presents a new task scheduling algorithm, called Potential Finish Time Min-mean Task Scheduling Algorithm (PFTSA), to enhance the selection of the suitable resources, which is responsible for the scheduling process. The proposed algorithm (PFTSA) schedules the tasks to the suitable resources by considering the potential finish time of the tasks, average execution time and waiting time of the tasks and average completion time of the resources. The proposed algorithm (PFTSA) results in minimum makespan as well as improved resource utilization. The experimental results indicate the PFTSA is a promising algorithm than the existing Min-min algorithm.