The Gravitational Search Algorithm (GSA) is a nature inspired optimization algorithm which is based on Newton's law of gravity and law of motion. Biogeography Based Optimization (BBO) is also another nature inspired optimization algorithm based on the concept of biogeography (migration and mutation among population). Both of these optimization technique are population based and individually have been applied to a large number of areas. In this paper, we are providing a hybrid GSABBO algorithm that will use the best properties of both the algorithm to enhance the exploration and exploitation properties and reach at the global optimal solution. Grid Computing refers to the sharing of resources across multiple domains to achieve a common goal. Sharing of the resources within an organization helps to enhance its overall performance computationally and economically. The advantages derived from Grid Computing are largely dependent on the scheduling algorithm we use to schedule various jobs across various resources available. This paper introduces a new approach based on the hybridization of BBO and GSA to generate optimal schedules to complete all the given tasks with minimum make span period.