Conventional fast continuous acquisition and denoising reconstruction methods of terahertz spectral signals mainly use Gauss high-order cumulant principle to calculate the signal reconstruction response coefficient, which is vulnerable to changes in the measurement matrix of signal samples, resulting in the reconstruction signal not fitting with the actual signal. Therefore, it is necessary to design a new fast continuous acquisition and denoising reconstruction method of terahertz spectral signals. That is to say, the terahertz spectral signal is smoothed, the characteristics of the terahertz spectral signal are extracted by using the multidimensional scaling method, and the fast acquisition and denoising reconstruction algorithm of the terahertz spectral signal is designed, thus completing the fast continuous acquisition and denoising reconstruction of the terahertz spectral signal. The experimental results show that the amplitude of the reconstructed signal of the designed fast continuous acquisition and denoising reconstruction method for terahertz spectral signal fits the actual signal, and the reconstructed signal to noise ratio is high, which proves that the designed fast continuous acquisition and denoising reconstruction method for terahertz spectral signal has good reconstruction effect, reliability, and certain application value.