Gravitational search algorithm (GSA) is a swarm intelligence based optimization algorithm which is based on the law of gravity and the law of motion of mass interaction between individuals. In GSA, the solution search process depends on the velocity which is a function of acceleration and the previous velocity. In the solution search process, acceleration plays important role and depends on the masses and forces of the individuals. Due to this component, GSA some times slow in convergence, while some time prematurely converge to the local optima. To avoid this situation, a new velocity update strategy is proposed, in which new velocity depends on the previous velocity and the acceleration, based on the fitness of the solutions. The proposed strategy is named as fitness based gravitational search algorithm (FBGSA). In FBGSA, the high fit solutions are motivated to exploit the promising search regions, while the low fit solutions have to explore the search space. Further, performance of the proposed strategy is compared with basic GSA and another swarm intelligence based algorithm, namely biogeography based optimization (BBO) algorithm over 16 different benchmark functions. Reported results show that FBGSA is a competitive variant of GSA algorithm.