Information-centric network (ICN) opens a new networking paradigm optimized for contents-oriented services by exploiting in-network caching and mitigating redundant transmissions. When such an ICN is deployed in mobile environments (i.e., the content provider or consumer is a mobile node), an appropriate mobility support protocol needs to be developed. Since the content consumer mobility can be tactically handled through the content consumer driven nature of ICN, the content provider mobility is investigated in this work. Specifically, we propose a proactive content pushing (PCP) scheme, in which the content provider proactively sends a set of contents that are expected to be requested in the near future to proximity ICN routers. Consequently, the PCP scheme can reduce the service disruption time owing to the content provider mobility.