On the basis of constructing the lookup-table of the backscattering efficiency factors of three wavelengths (355,532,1064 nm) and the extinction efficiency factors of two wavelengths (355 nm and 532 nm), the aerosol backscattering coefficients of three wavelengths and the extinction coefficients of two wavelengths (3β and 2α) are calculated. The inversion of spectrum distribution parameters of unimodal log-normal aerosol is simulated by nonlinear fitting. Results show that the spectrum distribution parameters of unimodal log-normal aerosol can be successfully inversed by this method. The effects of the different initial values on inversion results are small. The complex refractive index plays an important role in the inversion of the aerosol spectrum distribution. When the real and imaginary parts of the complex refractive index have the uncertainty of +1 and -1 step length respectively, the relative errors of the number concentration of particles, geometrical standard deviation and median radius are 20.32%, 33.50% and 24.72% respectively. The real part of the complex refractive index brings greater error than imaginary part. The study provides a theoretical foundation for the study of inversing vertical profile spectrum distribution of aerosol with multi-wavelength lidar.