The existence of gust interference, sensor noise, model uncertainty, nonlinear and underactuated characteristics of quadrotor drones, and unknown target drone motion poses challenges to the existing UAV dynamic interception technology based on image visual servoing (IBVS). Based on the image dynamics model of the virtual image plane and velocity compensation, this study designs a finite-time convergence interception control method. The incremental nonlinear dynamic inversion (INDI) technology is used to improve the robustness of the quadrotor drone to gust interference, unknown target acceleration and model uncertainty. From the comparison of simulation results, it can be seen that under the above environmental conditions, compared with the existing methods, the proposed control method improves the interception accuracy by 45%, 21.3% and 49.2% in the head-on interception, pursuit and maneuvering target interception tasks, respectively.