This paper investigates the angular velocity trajectory tracking problem for a DC permanent magnet motor with a DC-DC buck power converter based smooth starter. In practice, the composite control system is inevitably effected by unknown, exogenous, time-varying load torque disturbances. To this end, this paper specifically puts forward a disturbance rejection control approach. Under the proposed method, a novel disturbance observer is constructed to estimate the differences between actual states and the steady-state values of states and control. Therefore, an output feedback composite controller is designed. A key idea in the proposed control strategy is that the unmatched disturbances are transformed into matched ones ingeniously. The proposed control method is tested through simulation studies, where the results obtained validate the superiority of the proposed method.