This paper presents a proficient relay selection criterion for large-scale cooperative wireless networks (LSCWN) under Rayleigh fading, where each node in the network employs an Amplify and Forward (AF) relay protocol. We obtain analytic expression for Probability Density Function (pdf) and Cumulative Density Function (CDF) of end-to-end instantaneous signal-to-noise ratio and obtained minimized expression for the Moment Generating Function (MGF). The performance of the proposed relay selection criteria is analyzed and simulated. Simulation results shows an improvement in outage probability and symbol error rate by 63.88% and 84.89%, respectively, when the number of hops are increased from 1 to 3.