In order to improve the transient performance and system integration level of terahertz spectral analysis, this study proposes a novel terahertz spectrum-measurement method that combines metasurface spectral encoding and computational reconstruction. High-random spectral encoding of incident terahertz waves is achieved using spectral encoder devices that utilize multiple metasurface structures. Furthermore, a sparse recovery algorithm based on dictionary learning is developed to accurately restore the spectrum. Theoretical calculations and numerical simulations demonstrate that under a 4% noise level, the proposed method achieves a reconstruction error of less than 3% for the lactose transmission spectrum. Thus, the proposed method provides a new pathway for developing on-chip integrated terahertz spectrometers.