Shortwave infrared (SWIR) spectral imaging obtains spectral fingerprints corresponding to overtones of molecular vibrations invisible to conventional silicon-based imagers. However, SWIR imaging is challenged by the excessive cost of detectors. Single-pixel imaging based on compressive sensing can alleviate the problem but meanwhile presents new difficulties in spectral modulations, which are prerequisite in compressive sampling. In this work, we theoretically propose a SWIR single-pixel spectral imaging system with spectral modulations based on a Ge2Sb2Se4Te1 (GSST) phase-change metasurface. The transmittance spectra of the phase-change metasurface are tuned through wavelength shifts of multipole resonances by varying crystallinities of GSST, validated by the multipole decompositions and electromagnetic field distributions. The spectral modulations constituted by the transmittance spectra corresponding to the 11 phases of GSST are sufficient for the compressive sampling on the spectral domain of SWIR hyperspectral images, indicated by the reconstruction in false color and point spectra. Moreover, the feasibility of optimization on phase-change metasurface via coherence minimization is demonstrated through the designing of the GSST pillar height. The concept of spectral modulation with phase-change metasurface overcomes the static limitation in conventional modulators, whose integratable and reconfigurable features may pave the way for high-efficient, low-cost, and miniaturized computational imaging based on nanophotonics.