This paper deals with the finite-time distributed rotating encirclement control problem of multi-agent systems,where each agent tracks one target and every target can be tracked by one agent. Firstly, finite-time encirclement tracking protocols are designed for multi-agent systems, and these protocols contain observers for the geometrical center of the targets and estimators for the maximum distance between targets and their geometrical center. Secondly, sufficient conditions for achieving finite-time encirclement tracking are obtained. Finally,simulations are provided to demonstrate the effectiveness of the presented results.