Owing to advantageous feature of omnidirectional drive service robot (ODSR), i.e., simultaneous translation and rotation, the human-robot collaborations are more reliable and satisfactory. The path tracking model of an ODSR includes mechanism kinematics, mechanical dynamics with friction of each wheel and transformation between ODSR and world coordinates, and motor dynamics. To track the desired pose of ODSR in finite time, the adaptive finite-time virtual desired path (AFTVDP) is designed. To make the direct output track the AFTVDP in finite time, an adaptive finite-time control (AFTTC) is designed to execute high frequency motions. In summary, the proposed hierarchical adaptive finite-time control (HAFTC) contains AFTVDP and AFTTC. Finally, experiment validates the effectiveness of the proposed control.