In this paper, we numerically demonstrate efficient spectral compression (SPC) of wavelength-shifting soliton in a chalcogenide strip waveguide. It is found that the profiles of group-velocity dispersion (GVD) and Kerr nonlinearity play key roles in determining SPC. After calculating the dispersion of Kerr nonlinearity and Raman spectrum for three kinds of chalcogenide materials, Ge11.5As24Se64.5 is chosen as the material for designing the chalcogenide strip waveguide (CSW). The geometric parameters of CSW are optimized to obtain the desired GVD and Kerr nonlinearity. Simulation results show that in the designed CSW, an input spectrum width of 52.04 nm can be compressed to 7.23 nm along with wavelength shift of 17 nm when the input peak power is 25 W. With the input peak power increasing to 75 W, the SPC is slightly weakened, but wavelength shift can be up to 190 nm. The proposed CSW is applied to integrated all-optical quantization and an effective quantization number of 3.66-bit is achieved. It is expected that our research results can find important applications in on-chip integrated spectroscopy, all-optical signal processing, etc.