Mobile sinks can be a viable solution to solve the problem that energy consumption is not balanced for all the sensor nodes in Wireless Sensor Networks (WSNs). Frequent location updates from the sink (a current possible solution) can lead to both rapid energy consumption of the sensor nodes and increased collisions in wireless transmissions. This paper proposes a "Local Update-based Routing Protocol (LURP)" to help resolve this problem. When the sink node moves, it only needs to broadcast its location information within a local area rather than among the entire network. Both theoretical analysis and simulation studies show that LURP consumes less energy in each sensor node and also decreases the collisions in wireless transmissions, which can be used in large-scale WSNs.