This paper presents a novel optimal power demand management method for power consumers with an aggregator considering state and control constraints. The aggregator is an organization who manages some consumers to achieve demand response efficiently. This paper proposes a power demand adjustment method for the aggregator to allocate power reduction among consumers in a distributed manner. Specifically, this method simultaneously derives the optimal power reduction of each consumer using a gradient method and determines the control inputs by solving a quadratic programming problem with state and input constraint conditions. This paper also shows the convergence of the proposed algorithm, and finally, numerical simulation results illustrate the effectiveness of the proposed method.