Random Graphs evolved as a major tool for modelling the complex net works. Random Graphs have wide range of applications. Random Graph can be defined as a probability distribution over graph. Erdos Renyi Random Graph generation model is one of the most popular and best studied models of a network. Erdos Renyi Random Graph model G(n,p) generates random graph with n vertices where each edge appears with probability p. Despite the fact that the evolution of random graphs as data representation and modelling tool, the previous research hasn’t focused on the efficiency in generating random graphs. The Random Graph generation algorithms perform poor when generating massively large graphs and fails to use the parallel processing capabilities of modern hardware. The goal of my Thesis work is to parallelize the Random Graph generation models using GPGPU (General Purpose Graphics Processing Unit)to improve the performance