Felsenstein's maximum-likelihood approach for inferring phylogeny from DNA sequences assumes that the rate of nucleotide substitution is constant over different nucleotide sites. This assumption is sometimes unrealistic, as has been revealed by analysis of real sequence data. In the present paper Felsenstein's method is extended to the case where substitution rates over sites are described by the gamma distribution. A numerical example is presented to show that the method fits the data better than do previous models.