Since the discovery of the DNA Strand Displacement mechanism, researchers have implemented a lot of applications, such as DNA computing, DNA Circuits, Logic gates, and Chemical Reaction network. To achieve those functions, a well-designed system is essential, among which the toehold domains and migration domains play a vital role. In this paper, we designed three basic logic gates based on the toehold mediates DNA strand displacement mechanism, and utilized them to struct a three-layer multiplexer DNA logic circuit. However, the traditional INHIBIT gate annihilated all the inputs strands which obscure the multiplexer in further applications. Therefore, we improved the INHIBIT gate, so the desired input strand can be selected, and the corresponding output strand can be identified. Lastly, we adjusted the multiplexer and realized a cyclic DNA circuit. The simulation results verified the efficiency and reliability of our multiplexer DNA logic circuits. Our method has the ability in architecting complex DNA integrated circuits.INDEX TERMS DNA strand displacement, logic circuits, INHIBIT gate, demultiplexer.