A number of important applications related to complex network analysis require finding small vertex covers in massive graphs. This paper proposes an effective stochastic local search algorithm called DTS_MVC to fulfill this task. Relying on a fast vertex-based search strategy, DTS_MVC effectively explores the search space by alternating between a thresholding search phase during which the algorithm accepts both improving and non-improving solutions that satisfy a dynamically changing quality threshold, and a conditional improving phase where only improving solutions are accepted. A novel non-parametric operation-prohibiting mechanism is introduced to avoid search cycling. Computational experiments on 86 massive real-world benchmark graphs indicate that DTS_MVC performs remarkably well by discovering 7 improved best known results (new upper bounds). Additional experiments are conducted to shed light on the key ingredients of DTS_MVC.