Identifying influential nodes in complex networks has received increasing attention for its great theoretical and practical applications in many fields. Traditional methods, such as degree centrality, betweenness centrality, closeness centrality, and coreness centrality, have more or less disadvantages in detecting influential nodes, which have been illustrated in related literatures. Recently, the h-index, which is utilized to measure both the productivity and citation impact of the publications of a scientist or scholar, has been introduced to the network world to evaluate a node's spreading ability. However, this method assigns too many nodes with the same value, which leads to a resolution limit problem in distinguishing the real influence of these nodes. In this paper, we propose a local h-index centrality (LH-index) method for identifying and ranking influential nodes in networks. The LH-index method simultaneously takes into account of h-index values of the node itself and its neighbors, which is based on the idea that a node connects to more influential nodes will also be influential. According to the simulation results with the stochastic Susceptible-Infected-Recovered (SIR) model in four real world networks and several simulated networks, we demonstrate the effectivity of the LH-index method in identifying influential nodes in networks.