Security services such as authentication and pairwise key establishment are critical to sensor networks. They enable sensor nodes to communicate securely with each other using cryptographic techniques. In this paper, we propose two key predistribution schemes that enable a mobile sink to establish a secure data-communication link, on the fly, with any sensor nodes. The proposed schemes are based on the polynomial pool-based key predistribution scheme, the probabilistic generation key predistribution scheme, and the Q-composite scheme. The security analysis in this paper indicates that these two proposed predistribution schemes assure, with high probability and low communication overhead, that any sensor node can establish a pairwise key with the mobile sink. Comparing the two proposed key predistribution schemes with the Q-composite scheme, the probabilistic key predistribution scheme, and the polynomial pool-based scheme, our analytical results clearly show that our schemes perform better in terms of network resilience to node capture than existing schemes if used in wireless sensor networks with mobile sinks.