To guarantee secure communication in wireless sensor networks, secret keys should be securely established between sensor nodes. Recently, a simple key distribution scheme has been proposed for pair-wise key establishment in sensor networks by Anderson, Chan, and Perrig. They defined a practical attack model for non-critical commodity sensor networks. Unfortunately, the scheme is vulnerable under their attack model. In this paper, we describe the vulnerability in their scheme and propose a modified one. Our scheme is secure under their attack model and the security of our scheme is proved. Furthermore, our scheme does not require additional communication overhead nor additional infrastructure to load potential keys into sensor nodes.