The multi-object using Unmanned aerial vehicle, UAV monocular camera under object may have problems of position drift and failure of state prediction. To address these issues, a multi-object tracking method for UAV based on the thin plate spline function is proposed, the UAV motion is formulated by the space transformation function. The state space model for UAV motion is established, and the tracklets and detection correspondence are initialized by appearance characteristics. The unknown parameters of the model are obtained by calculating the least square solution of the thin plate spline function based on the initial correspondence. Then, the tracklets motion state is predicted according to the model. And the appearance to data association is combined. In addition, the space transformation parameters are introduced into the Kalman filter equation to realize the optimal estimation of tracklets state under camera motion. The process of tracklets initialization and termination, missed detection and false detection is realized by the effective tracklets management method. Experimental results on UAV data set show that the proposed algorithm has better performance than the existing state-of-the-art algorithms. Compared with the existing mainstream algorithm MDP, the multi-object tracking accuracy of the proposed algorithm is increased by 2. 75% .