A model of molecular evolution in which the parameter (intrinsic rate of amino acid substitution) fluctuates from time to time was investigated by simulating the process. It was found that the usual method of estimation such as Poisson fitting underestimates this variation of the parameter when remote comparisons are made. At the same time, four distance measures (minimun base difference, Poisson fitting, random nucleotide substitutions and negative binomial fitting) were tested for their accuracy. When the substitution rate is not uniform among the amino acid sites, the negative bionomial fitting gives most satisfactory results, however, one needs to know the parameter beforehand in order to use this method. It was pointed out that the fluctuation of the evolutionary rate is expected if the nearly neutral but very slightly deleterious mutations play an important role on molecular evolution.