Planar type docking enables a convenient underwater energy supply for irregularly shaped autonomous underwater vehicles (AUVs), but the corresponding control method is still challenging. Conventional control methods for torpedo-shaped AUVs are not suitable for planar type docking due to the significant differences in system structures and motion characteristics. This paper proposes a two-step adaptive control method to solve the planar type docking problem. The method makes a seamless combination of horizontal dynamic positioning and visual servo docking considering ocean current disturbance. The current disturbance is estimated and canceled in the pre-docking step using a current observer, and the positioning error is further compensated for by the vertical visual servo technique in the docking step. Reduced order dynamic models are distinctively established for different docking steps according to the motion characteristics, based on which the dynamic controllers are designed considering the model parameter uncertainties. Simulation is conducted with an initial distance of 10 m in the horizontal direction and 3 m in depth. Stable and accurate dynamic positioning under up to 0.4 m/s of current disturbances with different directions is validated. A 0.5 m lateral positioning error is successfully compensated for by the visual servo docking step. The proposed control method provides a valuable reference for similar types of docking application.