Modern online social networks and traditional face-to-face interactions are important social media for information spreading, and these two media are usually interconnected each other. We present a two-layer social network model to study the rumor spreading process. The model consists of two layers of networks with one layer is online social network (e.g. Facebook, Twitter and Sina Microblog, etc.) and the other is offline social network (also called as physical contact network, e.g. face-to-face communication). The rumor spreading dynamics under the interaction of online social network and offline social network is theoretical investigated. Through numerical simulations we find that the two-layered networks could enhance the spreading speed and expand the spreading scale under the action of online social network. Besides, although different network layers in the two-layered social network are interacted each other, the spreading rate in one layer only affects the spreading process within the same layer but almost have no effect on the spreading process in the other layer. Finally, the number of spreaders that transfers from offline social network is less effective than that from online social network.