Betweenness is a measure of the centrality of a node in a network, and is normally calculated as the fraction of shortest paths, random walk paths or flow units between node pairs that pass through the node of interest. Betweenness is, in some sense, a measure of the influence a node possesses over the spread of information in the network. However, the traditional betweenness is based on the information dissemination from one node to another. This is conceptually not suitable for the epidemics in which information is disseminated from one node to multiple neighboring nodes and destinations. To address this problem, we propose a novel betweenness measure based on epidemics. The epidemic betweenness counts the average number of the following nodes influenced by the node of interest after it becomes the epidemic source or an intermediary. This measure reflects the potential influence of a node to any epidemic in complex networks. To justify this measure, we introduce real complex networks and estimate the average influential scale of each node in epidemics through a large number of simulations. We compare the simulation results to those of the epidemic betweenness and another seven classic measures, such as Eigenvector and Katz. We further provide correlation studies to expose the differences of the epidemic betweenness in capturing influential nodes. We find that the epidemic betweenness is exclusively the measure that accurately present the potential influence of each node in epidemics. Finally, as an example of application, the epidemic betweenness measure explains the finding in recent research that unpopular users (nodes with small degree) could also lead to large cascades of epidemics.