In this paper, an attempt has been made to develop an Adaptive Social Acceleration Constant based PSO (ASACPSO). ASACPSO converge faster in comparison to basic PSO. The best value has been selected based on the minimum number of kounts required to minimize the function. Adaptive Social Acceleration Constant based PSO (ASACPSO) has been developed using the best value of adaptive social acceleration constant. The Adaptive Social Acceleration Constant has been searched using three formulations which led to the development of three algorithms-ALDPSO, AELDPSO-I and AELDPSO-II. All three were implemented on Rosenbrock   function to get the best value of adaptive social acceleration constant. Similarly it has been implemented on seven mathematical benchmark   functions and its performance has been compared to Basic Particle Swarm Optimization (BPSO). ASACPSO was observed to converge faster and give better accuracy. Results show that Kounts required for convergence of mathematical function is lesser for ASACPSO in comparison to basic PSO.ASACPSO reduces the computational time to optimize the function.