Computational grids have the potential for solving large-scale scientific applications using heterogeneous and geographically distributed resources. In addition to the challenges of managing and scheduling these applications, reliability challenges arise because of the unreliable nature of grid infrastructure. Two major problems that are critical to the effective utilization of computational resources are efficient scheduling of jobs and providing fault tolerance in a reliable manner. This paper addresses these problems by combining the checkpoint replication based fault tolerance mechanism with minimum total time to release (MTTR) job scheduling algorithm. TTR includes the service time of the job, waiting time in the queue, transfer of input and output data to and from the resource. The MTTR algorithm minimizes the response time by selecting a computational resource based on job requirements, job characteristics, and hardware features of the resources. The fault tolerance mechanism used here sets the job checkpoints based on the resource failure rate. If resource failure occurs, the job is restarted from its last successful state using a checkpoint file from another grid resource. Globus ToolKit is used as the grid middleware to set up a grid environment and evaluate the performance of the proposed approach. The monitoring tools Ganglia and Network Weather Service are used to gather hardware and network details, respectively. The experimental results demonstrate that, the proposed approach effectively schedule the grid jobs with fault-tolerant way thereby reduces TTR of the jobs submitted in the grid. Also, it increases the percentage of jobs completed within specified deadline and making the grid trustworthy.