A simple nearly neutral mutation model of protein evolution was studied using computer simulation assuming a constant population size. In this model, a gene consists of a finite number of codons and there is no recombination within a gene. Each codon has two replacement and one silent sites. The fitness of a gene was determined multiplicatively by amino acids specified by codons (the independent multicodon model). Nucleotide diversity at replacement sites decreases as selection becomes stronger. A reduction of nucleotide diversity at silent sites also occurs as selection intensifies but the magnitude of the reduction is not a monotone function of the intensity of selection. The dispersion index is close to one. The average value of Tajima's and Fu and Li's statistics are negative and their absolute values increases as selection intensifies. However, their powers of detecting selection under the present model were not high unless the number of sites is large or mutation rate is high. The MK test was shown to detect intermediate selection fairly well. For comparison, the house-of-cards model was also investigated and its behavior was shown to be more sensitive to changes of population size than that of the independent multicodon model. The relevance of the present model for explaining protein evolution was discussed comparing its prediction and recent DNA data.