Terahertz radar research has attracted widely attention of researchers due to its advantages such as short wave length, wide bandwidth, no blind spot, low power, and low intercept rate. It is generally considered that the echo signal of terahertz radar system is a signal with noise. Therefore, it is necessary to reduce the noise in the process of the frequency spectrum analysis of different-frequency signals. The fast Fourier transform (FFT) and the filtering method are commonly used in radar signal processing. The FFT method has lower ability to estimate the frequency of signal due to the interference noise. The filtering method detects the signal from the angle of noise elimination, but at the same time, it weakens useful characteristics, blurs position information about the signal, and affects detection capability of terahertz radar system. Aiming at the problem above, a method of detecting terahertz radar signals based on adaptive stochastic resonance (SR) system is proposed in this paper due to a phenomenon that the noise can be suppressed while amplifying the weak signal by transferring the noise energy after going through the SR system. With the different-frequency signal processing method of the twice sampling, the adaptive SR system and the scale recovery, the optimal parameters can be obtained automatically and the ranging calculation can be completed. Comparing with the FFT method, the mean output signal-to-noise ratio (SNR) gain through the SR system is 9.6843 dB at different measuring distances. When the measuring distance is 1000 mm, the initial spectrum value increases from 110.1 to 7172, which is 64.1 times higher than original value. The initial SNR of the whole system is improved from -11.94 to -0.179 dB, the gain is 11.761 dB. Comparing with the filtering method, the largest SNR gain is 6.485 dB when the measuring distance is 1000 mm, which is increased by 70.56%. When the input noise intensity is between 0.5 V and 1 V, the output SNR of the adaptive SR system is higher than that of the traditional filter system, but the gain is small and the maximum SNR gain is 2.148 dB. When the noise intensity of the system is between 1 V and 5 V, the SNR of the adaptive SR system is obviously higher than that of the filter system, and the largest SNR gain is 14.018 dB when the noise intensity D=5 V. The SNR curve of the adaptive SR system tends to be smoother and the curvature is 0.507, while the SNR curvature of the filtering model is 3.765, which is reduced by 86.5%. The method proposed in this paper not only solves the problem of noise coverage in the different-frequency signal, but also uses the characteristic that the noise energy can be transferred to the signal, to improve the output SNR of terahertz radar system, which is beneficial to further signal processing. Experimental results demonstrate that the ranging capability of the THz radar system is greatly improved, which has high application value and wide prospect in practical engineering research.