Abstract: The authors discuss the application of domain transformation acceptance-rejection method in Beta; vatiates and give the Beta variates algorithm generated by domain transformation acceptance-rejection method in the tail intervals and Patchwork method in central intervals. The experimental results show that the performance of this method is very close to that of the two common algorithms of Beta variates. The main strong points of this method lie in the fact that the sampling in tail intervals only adopts the concave property of Beta density function in this interval, while other algorithms need to adopt the special characteristics of this function.