Advanced control strategies critical for microrobots have been widely investigated to achieve precise locomotion. However, dynamic obstacle avoidance in 3D space is a major challenge in control that remains unsolved. In this work, a control scheme is developed for the automatic navigation of a helical microswimmer in 3-dimensional (3D) space with dynamic obstacles. A 3D hierarchical radar with a motion sphere and a detection sphere is firstly developed. Using the radar-based avoidance approach, the desired motion direction for the microswimmer to avoid obstacles can be obtained, and the coarse-to-fine search is used to decrease the computational load of the algorithm. Three navigation modes of the microswimmer in 3D space with dynamic conditions are realized by the radar-based navigation strategy that combines the global path planning algorithm and the radar-based avoidance approach. Subsequently, a motion controller is proposed to achieve precise 3D locomotion control of the microswimmer. The control scheme integrating the radar-based navigation strategy and the motion controller is developed. The experimental results of navigated locomotion of a helical microswimmer in 3D space with 8 static obstacles and 8 dynamic obstacles demonstrate the effectiveness of the control scheme, and the proposed control scheme paves the way for advanced locomotion control of helical microswimmers in complex 3D space.