The algorithm of Minh as in [Minh (1988)] was used to generate variates having a gamma distribution with shape parameter a>1 only. In this paper, a method, which is the improvement of the algorithm of Minh is introduced for the generation of independent random variables from a gamma distribution with all values of shape parameter and is compared with the method of Marsaglia and Tsang. By means of computer simulation, for each method and each value of shape parameter, a series of 10.000 gamma variables was generated, and then the speed, the randomness and the preservation of the numerical characteristics, namely expected value, variance and skewness coefficient are considered. It is found that the speed and the randomness of the two methods are the same, however, the preservation of the numerical characteristics of the gamma distribution by the proposed method is much better than the method of Marsaglia and Tsang.