In this paper, we propose an efficient concurrent wait-free algorithm to construct an unbounded directed graph for shared memory architecture. To the best of our knowledge that this is the first wait-free algorithm for an unbounded directed graph where insertion and deletion of vertices and/or edges can happen concurrently. To achieve wait-freedom in a dynamic setting, threads help each other to perform the desired tasks using operator descriptors by other threads. We also prove that all graph operations are wait-free and linearizable. We implemented our algorithms in C++ and tested its performance through several micro-benchmarks. Our experimental results show an average of 9x improvement over the global lock-based implementation. © 2019 IEEE.