The analytic function for the amplified spontaneous emission spectrum of InP/InGaAsP multi-quantum wells is studied by spectrum fitting. Three fitting functions, Lorentz, Gaussian and Sech line shape functions are chosen, and the analytical expressions for the above three functions are obtained with Levenberg-Marquardt algorithm, respectively. The center wavelength of Lorentz line shape function spectrum fitting is 1548.707 nm with 66.23 nm of full-width half maximum (FWHM), -0.00036484 mW power compensation, 0.98294 of R-square and 4.7674310-6 of residual sum of squares; the center wavelength of Gaussian line shape function spectrum fitting is 1548.651 nm with 61.42 nm of FWHM, 0.00212 mW power compensation, 0.99191 of R-square and 2.2650510-6 of residual sum of squares; the center wavelength of Sech line shape function spectrum fitting is 1548.787 nm with 36.99 nm of FWHM, 0.00222 mW power compensation, 0.98128 of R-square and 5.2433110-6 of residual sum of squares. It can be seen that Gaussian line shape function spectrum fitting has the highest R-square and smallest residual sum of squares, and the residual squares of data are symmetrically distributed among 0.0001. Gaussian line shape function spectrum fitting has higher fitting degree. It is demonstrated that InP/InGaAsP multi-quantum wells is a kind of active layer quantum well structure semiconductor material, whose amplified spontaneous emission spectrum line shape belongs to inhomogeneous broadening due to the effect of lattice defects, the corresponding line shape function is Gaussian line shape function, and the amplified spontaneous emission spectrum line shape function can be used for designing the optical passive devices.