An analytic method for a complementary metal-oxide-semiconductor (CMOS) terahertz plasmon detector operating in the subthreshold region is presented using the equivalent circuit model. With respect to design optimization of the detector, the signal transmission from the antenna port to the output of the detector is described by using the proposed circuit model, which does not include a complicated physical operating principle and mathematical expressions. Characteristics from the antenna port to the input gate node of the detector are analyzed through the superposition method by using the characteristic impedance of transmission lines. The superposition method shows that the effect of interconnection lines at the input is simplified with the optimum bias point. The characteristics of the plasmon detection are expressed by using small-signal analysis of the single transistor at the sub-threshold operation. The results of the small-signal analysis show that the unity gain preamplifier located between the detector core and the main amplifier can improve the detection performances such as the voltage responsivity and the noise equivalent power. The measurement results using the fabricated CMOS plasmon detector at 200 GHz suggest that the unity gain preamplifier improves the detector performances, which are the same results as we received from the proposed analytic method.