Abstract: Alpha stable distribution is one of the best non-Gaussian probability models for underwater acoustics rever-beration data. Numerical simulation of Alpha Stable Distribution sequence, which obeys the standard parameter system, is the basis of the corresponding research. The transformation relationship among Alpha Stable Distribution random variables under the three parameter systems and the advantages and disadvantages of various parameter system formu-lations are summarized. Under the standard parameter system the numerical simulation of Alpha stable distribution sequence with of arbitrary parameter combination is implemented. Without explicit probability density expression, the probability density values of Alpha Stable Distribution are calculated with direct numerical integration method, which are used as theoretical values to make comparative analysis with statistical ones, and to verify the correctness of the numerical simulation method.