In this paper, we investigate a predator-prey population modeled by a system of differential equations modified Leslie-Gower and Holling-Type II schemes with time-dependent parameters. We establish a sufficient criterion posed on the behavior at infinity of coefficients for the permanence of systems, globally asymptotic stability of solutions. In the case where the coefficients of equations are periodic functions with a same period, it is proved that there exists a unique periodic orbit which attracts every solution starting in $\mathrm{int}\,\mathbb R^2_+$.