Recently, sink mobility is introduced to balance energy consumption in WSNs. However, mobile sinks are required to inform potential sources about their new location information whenever necessary. Frequent location updates can cause both increased transmission traffic and rapid energy consumption. This paper presents a novel data-gathering scheme for WSNs with a single mobile sink to minimize the overhead of location updates. The main novelty of our proposed data gathering scheme is that, by constructing a virtual binary-tree infrastructure in the deployment area and introducing the direction value of the sink in the binary-tree infrastructure, each node can obtain sink location easily with little location update consumption whenever necessary. Additionally, our proposed scheme can also keep the data uploading of nodes continuous while the sink changes its location, which reduces the number of dropped packets. Simulation results show that our proposed scheme effectively reduces the energy consumption and packet loss rate, thereby extending the network lifetime as expected.