In recent years, grid technology has emerged as an important tool for solving compute-intensive problems within the scientific community and in industry. Grid reliability analysis and modeling are not easy tasks because of the complexity and large scale of the system. While concerning on large scale system, large subtasks requires time-consuming computation, consequently the reliability of grid service could be rather low. However, efforts are in progress to develop reliability methods for grid environments that are expected have increased scale, heterogeneity, and dynamism. Our paper tries to focus on this reliability and task scheduling in the grid. In the existing system all researchers focused on the remote node fault recovery where greater waste is consumed on time and resource. Furthermore those systems did not incorporate the fault recovery and the practical constraints of grid resource on optimization. Resultantly our paper considers the Local Node Fault Recovery (LNFR) mechanism into grid systems, and presents a solution to simultaneously maximize the grid service reliability modeling and analysis with this kind of fault recovery thereby minimizing the cost. Our proposed LNFR mechanism considers some practical, some constraints such as the life times of subtasks, the numbers of recoveries performed in grid nodes, and thus grid service reliability models under these practical constrictions are developed. Presuming the proposed grid service reliability model, a multi-objective task scheduling optimization model is presented, and Min Max scheduling algorithm is developed to solve it effectively. Result shows that our proposed system is cost effective and in future will be extended still which could be applied in cloud computing domains.