WiFi networks have been deployed in many regions such as buildings and campuses to provide wireless Internet access. However, to support ubiquitous wireless service, one possibility is to integrate these narrow-range WiFi networks with a wide-range network such as WiMAX. Under this WiMAX-WiFi integrated network, how to conduct energy-efficient handovers is a critical issue. In this paper, we propose a handover scheme with geographic mobility awareness (HGMA) by considering the past handover patterns of mobile devices. HGMA can conserve the energy of handovering devices from three aspects. First, it prevents mobile devices from triggering unnecessary handovers by measuring their received signal strength and moving speeds. Second, it includes a handover candidate selection (HCS) method for mobile devices to intelligently select a subset of WiFi access points or WiMAX relay stations to be scanned. Therefore, mobile devices can reduce their network scanning and thus save their energy. Third, HGMA prefers mobile devices staying in their original WiMAX or WiFi networks. This can prevent devices from consuming too much energy on interface switching. Simulation results show that HGMA can reduce about 69% and 30% of energy consumption on network scanning and interface switching, respectively, and with 16% to 64% more probabilities for mobile devices staying in WiFi networks.