The intensity fluctuation induced spectral phase-change of the laser pulse during nonlinear spectral broadening is theoretically investigated. The oscillation of the phase-change curves at the central part of the spectra is explained by the two-wave interference model, while the bending of the phase-change curves at the wings is considered to originate from the intensity dependent dispersion caused by the self-steepening (SST) effect. Both of them can degrade carrier envelop phase (CEP) stability after an intra-pulse difference frequency generation (IP-DFG) setup. We propose an effective approach to suppress the intensity dependent dispersion with intermediate compression. Verified by numerically simulations, well-phased spectral components at the wings can be obtained, which is highly beneficial for CEP stable pulse generation with noisy input.