Counting triangles in a large network is an important research task because of its usages in analyzing large networks. However, this task becomes expensive when runs on large networks with millions of nodes and millions of edges. For efficient triangle counting on such networks, researchers in recent years have adopted approximate counting or have proposed parallel or distributed solutions. In this work, we propose an approximate triangle counting algorithm, that runs on multi-core computers through a multi-threaded implementation. We show that for a given speedup factor, our method has a better approximation accuracy; further, the multi-threaded implementation that we propose is much superior to the Hadoop based distributed methods that earlier algorithms propose.