Wireless sensor networks have been widely used in a variety of domains which include military sensing and tracking, patient monitoring and health care, etc. When sensor networks are deployed in a hostile environment, security becomes extremely important, as they are vulnerable targets to different types of malicious attacks. Due to the wireless property of sensor devices, the sensor networks may easily be compromised by attackers who modify messages or provide misleading information to other sensor nodes. Therefore, the security of the sensor networks is very important. This paper will present a new efficient key pre-distribution scheme for secure wireless sensor networks. It provides an approach that any pair of sensor nodes can find a common pairwise secret key between them with simple calculation. Compared with previously proposed key pre-distribution schemes, the proposed method could reduce large amounts of computations and communications in both the key pre-distribution step and finding a common secret key for any pair of nodes to achieve secure connectivity.