Pairwise key establishment is one of the fundamental security services in sensor networks which enables sensor nodes in a sensor network to communicate securely with each other using cryptographic techniques. It is not feasible to apply traditional public key management techniques in resource-constrained sensor nodes, and also because the sensor nodes are vulnerable to physical capture. In this paper, we introduce a new scheme called the identity based key pre-distribution using a pseudo random function (IBPRF), which has better trade-off between communication overhead, network connectivity and resilience against node capture compared to the other key pre-distribution schemes. Our scheme can be easily adapted in mobile sensor networks. This scheme supports the addition of new sensor nodes after the initial deployment and also works for any deployment topology. In addition, we propose an improved version of our scheme to support large sensor networks.