We obtain a sufficient condition for the global attractivity of the genotype selection model y n + 1 = y n e β n ( 1 − 2 y n − k ) / ( 1 − y n + y n e β n ( 1 − 2 y n − k ) ) , n ∈ ℕ . Our results improve the results established by Grove et al. (1994) and Kocić and Ladas (1993).