Coverage, energy efficiency and connectivity are important metrics for sensor network deployment. In this paper, we propose a relay shift based approach to eliminate coverage hole due to the initial random dropping or the existence of faulty sensors. The sensors in our model are assumed to have only limited mobility. Firstly, the optimal number of clusters are determined by energy function and the optimal cluster head positions are determined by Fuzzy C-mean (FCM). We use proposed Relay Shift Based Algorithm (A*-RSBA) for movement assisted sensor deployment. A* algorithm is applied to find a shortest path from a redundant sensor node to a virtual node point in an uncovered area, and each sensor moves along this path by relay shift based on the principle that evenly distributed sensors can provide better coverage. Simulation results show that our approach can improve coverage within a short time and limited movement distance as well as ensuring connectivity and energy efficiency.