The minimum vertex cover (MVC) problem is a canonical NP-hard combinatorial optimization problem, aiming to find a smallest set of vertices such that every edge has at least one endpoint in the set, which has extensive applications in cyber security, scheduling, and monitoring link failures in wireless sensor networks (WSNs). Numerous local search algorithms have been proposed to obtain a “good” vertex cover. However, due to the NP-hard nature, it is challenging to efficiently solve the MVC problem, especially on large graphs. In this paper, we propose an efficient local search algorithm for MVC called TIVC, which is based on two main ideas: A 3-improvements (TI) framework with tiny perturbation, and an edge selection strategy. We conducted experiments on real-world large instances of a massive graph benchmark. Compared with two state-of-the-art MVC algorithms, TIVC shows superior performance in accuracy and possesses a remarkable ability to identify significantly smaller vertex covers on many graphs.