This study is concerned with the predefined-time control issue, where the system settling time is required to be within a predefined value determined by the control parameter. Aiming at the overload control and singularity problem in the classical predefined-time control, we propose a novel nonsingular predefined-time control method with dynamic parameter. Specifically, the overload control problem refers that the fixed and small control parameter, which exactly reflects the maximum system settling time, would result in large control requirement due to relatively large initial error. This increases control energy consumption or even cannot be satisfied due to actuator saturation in practice. The time-varying parameter designed in this paper is effective to solve this problem. Moreover, an auxiliary segmentation term is embedded to the control law to further avoid singularity. Subsequently, the predefined-time control is applied within the visual target tracking scenario for UAVs. Finally, we conduct comparative numerical simulations and hardware-in-the-loop simulations for the purpose of validating the effectiveness and advantages of the presented method.