A novel two-stage spectral compression structure which employs a logarithmic dispersion increasing fiber (DIF) interconnected with a highly nonlinear linear fiber-nonlinear optical loop mirror (HNLF-NOLM) is proposed and demonstrated by numerical simulation. The numerical simulation is implemented by solving the generalized nonlinear Schrodinger equation using split-step Fourier method, where the soliton number is in the range of 0.5≤N≤1.4. The results show that the spectra are well-compressed and low-pedestal, and the maximum spectral compression ratio (SCR) can reach 10.93 when N=1.4.