In practice，various non-Gaussian signals and noises have distinct spiky and impulsive characteris-tics，leading them to deviate from Gaussian distribution，while Alpha stable distribution is the useful tool of these processes． This paper mainly studies the generation of random variables subject to the alpha stable distribution inthe standard parameters and carries on the simulation． Firstly，based on the basic theories of the Alpha stable dis-tribution，we analyze the commonly used parameterizations and the conversion relationship of related parameters，asthe theoretical basis of this study． Secondly，we provide the generation of random variables based on Standard Pa-rameterization，and then use MATLAB for simulating． At the end of the paper，simulation experiments verify thefeasibility of the algorithm．