Abstract: In view of the non-Gaussian of ocean ambient noise, the a stable distribution is applied to the statistical modeling. Firstly, the correspondence between the model characteristic exponent and the sample kurtosis is established based on the similarity in physical meaning of the two. And the kurtosis of the sum of two independent random variables is deduced, and this can be used to explain the kurtosis characteristic of interfered background noise. Secondly,some numerical simulations are made to model samples with higher and lower kurtosis than three, the results show good adaptability in leptokurtic distribution. Finally, three typical samples are taken under quiet environment, air gun interference and ship interference environment. Their Gaussianities are judged by the Quantile Quantile plot. And then the four parameters of the model are estimated by the quantile based method and characteristic function based method jointly of the three categories. The statistical law of the characteristic exponent is emphatically analyzed:in the quiet environment, the characteristic exponent is close to 2.0, which is the value of Gaussian model;but for the air gun data,it is between 1.2 and 1.7, which means leptokurtic;and under the interference of the sailing ship, the value of a is related to the ship speed and the distance from the ship source to the receiving location, the more significant the ship impact is, the smaller the characteristic exponent is, which is consistent with the variation of kurtosis of disturbing noise in physical meaning. The results of the model verification show that the a stable distribution behaves well under the above three kinds of trial conditions, especially for the air gun environment which is far superior to the normal distribution.