Recently, information transmission models motivated by the classical epidemic propagation, have been applied to a wide-range of social systems, generally assume that information mainly transmits among individuals via peer-to-peer interactions on social networks. In this paper, we consider one more approach for users to get information: the out-of-social-network influence. Empirical analyses of eight typical events' diffusion on a very large micro-blogging system, \emph{Sina Weibo}, show that the external influence has significant impact on information spreading along with social activities. In addition, we propose a theoretical model to interpret the spreading process via both internal and external channels, considering three essential properties: (i) memory effect; (ii) role of spreaders; and (iii) non-redundancy of contacts. Experimental and mathematical results indicate that the information indeed spreads much quicker and broader with mutual effects of the internal and external influences. More importantly, the present model reveals that the event characteristic would highly determine the essential spreading patterns once the network structure is established. The results may shed some light on the in-depth understanding of the underlying dynamics of information transmission on real social networks.