A typical hybrid cloud connects a private data center to a portion of a public cloud. It can potentially scale up the computing pool of a private cloud on demand. This work presents a novel adaptive computing framework that enables intelligent automatic application migration between a private data center and a public cloud. In the case that the workload of the private data center is too high, the proposed framework can create more computing resources in the public cloud automatically, and then move applications to the public cloud in order to reduce the workload of the private data center. The proposed framework employs the multi-agent technique to manage all resources, monitor system behavior, and negotiate all actions in the hybrid cloud. We have built a prototype of a hybrid cloud environment to demonstrate that the proposed framework is able to perform intelligent application migration and self-provisioning.