In this paper, we propose an approach to design reduced-order state observer for Boolean control networks by applying the semi-tensor product. At first, an approach is given to find reducible state variables. After that, we introduce an approach for reduced-order observer design based on the reducible state variables. Then, it is shown that similar to the Luenberger-like observer, the state estimate provided by the reduced-order observer also converges to real state at time not later than the minimal reconstructibility index. Additionally, the reduced-order observer requires lower computational effort, which facilitates an online implementation.