This paper deals with a novel research work about a new efficient approximation algorithm for influence maximization, which was introduced to maximize the benefit of viral marketing. For efficiency, we devise two ways of exploiting the 2-hop influence spread which is the influence spread on nodes within 2-hops away from nodes in a seed set. Firstly, we propose a new greedy method for the influence maximization problem using the 2-hop influence spread. Secondly, to speed up the new greedy method, we devise an effective way of removing unnecessary nodes for influence maximization based on optimal seed’s local influence heuristics. In our experiments, we evaluate our method with real-life datasets, and compare it with recent existing methods. From experimental results, the proposed method is at least an order of magnitude faster than the existing methods in all cases while achieving similar accuracy.