Coherent anti-Stokes Raman scattering (CARS) imaging of femtosecond pulses has been a research hotspot in recent years, but the wide spectrum of the femtosecond pulse limits the spectral resolution of CARS imaging. Spectral compression is considered as an effective method to solve this problem. In this work, an all-fiber chirp spectral compression method of graded-index multi-mode fiber/single-mode fiber (GI-MMF/SMF) structure based on fiber pre-chirp and self-phase modulation is presented. It can be used as a CARS excitation source to increase the spectral resolution of CARS imaging. In the section of numerical simulation, the mean group velocity dispersion value of GI-MMF is used as a numerical parameter of the chirp analysis, which is estimated by analyzing modes of GI-MMF. On one hand, the mode field distributions in GI-MMF are simulated numerically by the finite-difference time-domain method, and these different modes are divided into eight mode groups. On the other hand, the energy proportion of each mode group is regarded as a weight value. Then we can obtain a mean group velocity dispersion value of 50/125 m GI-MMF, which is -2.28710-5 fs2/nm, by calculating the sum of group velocity dispersion weight values of mode groups. The results of spectral compression with different length ratios of 50/125 m GI-MMF to 780HP SMF are also analyzed based on the generalized nonlinear Schrdinger equation and split-step Fourier algorithm. The spectral width of 2.486 nm and the compression ratio of 5.230 are calculated, when the length ratio of 50/125 m GI-MMF to 780HP SMF is 1.2. In the section of experiment, three kinds of GI-MMFs with different core diameters are used in the experiment, the influences of the core diameter and the length ratio of GI-MMF to 780HP SMF on the spectral compression are investigated. The results show that the spectral width of 2.243 nm, corresponding to the compression ratio of 5.796 is obtained, when the length ratio of 50/125 m GI-MMF to 780HP SMF is 1.2, which is consistent with the simulation result. Under the condition of the same length ratio, the use of 105/125 m GI-MMF can raise the compression ratio to 152.941, and the spectral width of output pulse is 0.085 nm. When the pulse is applied to CARS spectrum detection, the theoretical spectral resolution can be 1.386 cm-1. The experimental results show that the spectral compression way to improve spectral resolution of CARS imaging is effective. This spectral compression system is characterized by simple structure, and high and controllable compression ratio, which provides theoretical and experimental basis for the all-fiber high spectral resolution CARS excitation source research.