We consider a special discrete time Leslie-Gower competition models for three species: $ x_i(t+1) = \frac{a_ix_i(t)}{1+x_i(t) +c \sum_{j\not = i} x_j(t)} $ for $ 1\leq i \leq 3 $ and $ t \geq 0 $. Here $ c $ is the interspecific coefficient among different species. Assume $ a_1>a_2>a_3>1 $. It is shown that when $ 0<c< c_0: = (a_3-1)/(a_1+a_2-a_3-1) $, a unique interior equilibrium $ E^* $ exists and is locally stable. Then from a general theorem in Balreira, Elaydi and Luis (2017), it follows that $ E^* $ is globally asymptotically stable. Using a result of Ruiz-Herrera [
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