The armature controlled DC motor is widely used in modern industry and technology, and its output performance directly affects the efficiency and stability of the whole system. Thus, it is of great theoretical and practical significance to study the output constraint of an armature controlled DC motor. To this end, this paper presents the angular velocity control of an armature controlled DC motor with output and state constraints. To guarantee the constraints on output and state as well as the stability of the system, integral barrier Lyapunov function is constructed and backstepping control method is adopted. And hence, we achieve the angular velocity tracking the expected value and the output keeps in the predetermined range, moreover output tracking error is constrained by decreasing exponentially over time. Finally, the desired angular velocity is taken as constant speed, uniform change and sine law change cases in the simulation experiment, which results further prove the effectiveness of the method.