Measurements of bubble size distribution require the understanding of the acoustic characteristics of the medium. The bubbles show highly nonlinear properties under finite amplitude acoustic excitation, so the acoustic fields from bubble population are easily observed at the second harmonics as well as at the fundamental frequency, which shows that the nonlinear coefficient increases obviously. The inversion method of bubble size distribution based on nonlinear acoustic effects can peel off the influence of complex environment and obtain the size distribution coefficient information of bubbles more accurately. The previous nonlinear inversion methods of bubble size distribution are mostly based on the nonlinear scattering cross-section characteristics of bubbles. However, the stability of inversion is not high enough. In this paper, we introduce a new acoustic inversion method for bubble size distribution, which is based on the nonlinear coefficients of bubble medium. Compared with other inversion methods based on linear or nonlinear scattering cross section, the inversion method based on nonlinear coefficients of bubble medium proposed in this paper shows good robustness in both simulation and experiment.