Key management is considered to be the prerequisite for secure communication in WSNs. However, many of those key management schemes normally either require the predeployment knowledge to generate keys, which is unrealistic, especially in large scale sensor networks, or consume a large amount of energy. In this paper, we present a new key management scheme named Energy-efficient Location-dependent Key Management scheme (ELKM). ELKM generates keys for each node based on their relative locations. Based on loose time synchronization, ELKM reduces energy consumption significantly on the total size of transmitted message comparing with previous works. The performance analysis shows that ELKM guarantees high security level and good network connectivity. Simulation results demonstrate that ELKM consumes less energy compared with LDK.