It remains a challenge to stabilize a nonlinear system while satisfying time-varying state constraints for safety. In this study, we developed a time-varying nonlinear control barrier function (TVNCBF) approach to stabilize a nonlinear system with high-relative-degree state constraints. This approach mitigated potential conflicts among multiple control barrier function constraints, providing a theoretical foundation for safety control of affine nonlinear systems. We then proposed a safety control strategy for nonlinear systems and comprehensively analyzed its safety and feasibility. At the same time, considering a scenario where an unmanned aerial vehicle (UAV) avoids several dynamic obstacles during target tracking, we designed a direct safety control for the UAV system to ensure safe target tracking. Simulation results demonstrated the safety and stability of the UAV system under the proposed control strategy.