Hybridization of two or more variants of algorithms is the recent trend of the research field. With the help of a hybridized algorithm we try to find out the better optimal solution and to solve various optimization applications. In this paper, a new approach Advancement on Grey Wolf Optimization with Fitness Based Self Adaptive Differential Evolution (AGWO-FSADE) is proposed. Fitness of populations are calculated using the self adaptive strategy of FSADE and updated by GWO algorithm. FSADE algorithms balance the convergence and diversity capability and due to fine tuning of Crossover Probability CR and Scale Factor F therefore, in large step size very less chance to skip the actual solutions. The performance of AGWO-FSADE is measured by 19 Benchmark functions and compared with classic GWO, ABC and PSOGWO algorithm. The results are more accurate to solve these functions. Keywords - nature inspired algorithm, self adaptive technique, grey wolf optimizer, fitness based self adaptive differential evolution, optimization technique