PageRank is a well-known algorithm whose robustness helps set a standard benchmark when processing graphs and analytical problems. The PageRank algorithm serves as a standard for many graph analytics and a foundation for extracting graph features and predicting user ratings in recommendation systems. The PageRank algorithm iterates continuously, updating the ranks of the pages till convergence is achieved. Nevertheless, the implementation of the PageRank algorithm on large-scale graphs that on shared memory architecture utilizing fine-grained parallelism is a difficult task at hand. The experimental study and analysis of the Parallel PageRank kernel on large graphs and shared memory architectures using different programming models have been studied extensively. This paper presents the asynchronous execution of the PageRank algorithm to leverage the computations on massive graphs, especially on shared memory architectures. We evaluate the performance of our proposed non-blocking algorithms for PageRank computation on real-world and synthetic datasets using Posix Multithreaded Library on a 56 core Intel(R) Xeon processor. We observed that our asynchronous implementations achieve 10x to 30x speedup with respect to sequential runs and 5x to 10x improvements over synchronous variants.