Bio-inspired magnetic helical microrobots have great potential for biomedical and micromanipulation applications. Precise interaction with objects in liquid environments is an important prerequisite and challenge for helical microrobots to perform various tasks. In this study, an automatic control method is proposed to realize the axial docking of helical microrobots with arbitrarily placed cylindrical objects in liquid environments. The docking process is divided into ascent, approach, alignment, and insertion stages. First, a 3D docking path is planned according to the positions and orientations of the microrobot and the target object. Second, a steering-based 3D path-following controller guides the helical microrobot to rise away from the container bottom and approach the target along the path. Third, based on path design with gravity compensation and steering output limits, alignment of position and orientation can be accomplished simultaneously. Finally, the helical microrobot completes the docking under the rotating magnetic field along the target orientation. Experiments verified the automatic docking of the helical microrobot with static targets, including connecting with micro-shafts and inserting into micro-tubes. The object grasping of a reconfigurable helical microrobot aided by 3D automatic docking was also demonstrated. This method enables precise docking of helical microrobots with objects, which might be used for capture and sampling, in vivo navigation control, and functional assembly of microrobots.