In this paper, we introduce a translational force control method with disturbance observer (DOB)-based force disturbance cancellation for precise three-dimensional acceleration control of a multi-rotor UAV. The acceleration control of the multi-rotor requires conversion of the desired acceleration signal to the desired roll, pitch, and total thrust. But because the attitude dynamics and the thrust dynamics are different, simple kinematic signal conversion without consideration of those difference can cause serious performance degradation in acceleration tracking. Unlike most existing translational force control techniques that are based on such simple inversion, our new method allows controlling the acceleration of the multi-rotor more precisely by considering the dynamics of the multi-rotor during the kinematic inversion. By combining the DOB with the translational force system that includes the improved conversion technique, we achieve robustness with respect to the external force disturbances that hinders the accurate acceleration control. mu-analysis is performed to ensure the robust stability of the overall closed-loop system, considering the combined effect of various possible model uncertainties. Both simulation and experiment are conducted to validate the proposed technique, which confirms the satisfactory performance to track the desired acceleration of the multi-rotor.