In this work, the global behavior of a discrete population model

$$\{\begin{array}{ll}{x}_{n+1}& =\alpha x_n{e}^{-y_n}+\beta ,\\ y_{n+1}& =\alpha x_n(1-e^{-y_n}),\end{array}n=0,1,2,\dots ,$$

is considered, where $\alpha \in (0,1)$, $\beta \in (0,+\mathrm{\infty })$, and the initial value $(x_0,y_0)\in [0,\mathrm{\infty })\times [0,\mathrm{\infty })$. To illustrate the dynamics behavior of this model, the boundedness, periodic character, local stability, bifurcation, and the global asymptotic stability of the solutions are investigated.