With the development of the information and Internet technology, the public opinions with big data will rapidly emerge in an online-offline social network, and an inefficient management of public opinions often will lead to the security crisis for either firms or governments. To unveil the interaction mechanism among a large number of agents between the online and offline social networks, in this paper we propose the public opinion dynamics model in an online-offline social network context. Next, in the theory aspect we investigate the analytical conditions to form a consensus in the public opinion dynamics model. Furthermore, we conduct the extensive simulations to investigate how the online agents impact the dynamics of public opinion formation, and unfold that the online agents shorten the steady-state time, decrease the number of opinion clusters, and smoothen the opinion changes in the opinion dynamics. The increase in the size of the online agents often enhances these effects. The results in this paper can provide a basis for the management of the public opinions in the Internet age.