Most of wireless sensor networks (WSNs) are deployed in hostile environments where communication between sensors may be monitored. For applications that require higher data security, employing some cryptographic scheme is therefore necessary in the networks. However, key management in WSNs is a challenging task due to resource constraints on sensor nodes. In this paper, based on the concept of small worlds, we present a group-based key pre-distribution scheme which enables any pair of sensors to establish a unique shared key. The proposed method for key path establishment uses only local information with logarithmic memory overhead to the number of groups. We also evaluate other performance aspects, including communication and computing overhead. The analysis and simulation results show that the proposed key management method performs better than other known methods.