The Gravitational search algorithm (GSA) is categorized in swarm intelligence optimization techniques, based on the Newton's law of gravity and motion. In GSA, solution look process relays on the velocity, which is an element of acceleration that decides the step size of the solutions. Due to this component, sometimes the global search process may skip the global optima. So, to avoid this situation, this paper presents a local exploitation based gravitational search algorithm (LEGSA), in which acceleration represented in the form of gravitational field and it reduces iteratively. Due to this, solutions are motivated to exploit more desirable in search space. Further two control parameter, Kbest and gravitational constant are also modified, to give a proper balance amongst exploration and exploitation capabilities. The proposed LEGSA are examined on the 16 different benchmark functions. A Local Exploitation Based GSA (LEGSA) has obvious advantages in comparison with the traditional Gravitational search algorithm (GSA) and Biogeography-based optimization (BBO) algorithm.