Summary: By using Mawhin’s coincidence degree theory, we study the existence of a positive periodic solution to the following genotype selection model \[ x_{n+1}=\frac {x_n \exp[\beta_n (1-\alpha x_{n-k})]}{1-x_n+x_n\exp[\beta_n (1-\alpha x_{n-k})]} , \, n=0, 1, 2, \cdots \] and obtain a new sufficient condition for the existence of positive periodic solution of the difference model.