Summary: We explore the local dynamics, N-S bifurcation, and hybrid control in a discrete-time Lotka-Volterra predator-prey model in \(\mathbb{R}_+^2\). It is shown that \(\forall\) parametric values, model has two boundary equilibria: \( P_{00}(0, 0)\) and \(P_{x 0}(1, 0)\), and a unique positive equilibrium point: \( P_{x y}^+ \left( \frac{d}{c}, \frac{r(c-d)}{bc}\right)\) if \(c > d\). We explored the local dynamics along with different topological classifications about equilibria: \(P_{00}(0,0), P_{x 0}(1,0)\), and \(P_{xy}^+ \left(\frac{d}{c}, \frac{r(c-d)}{bc}\right)\) of the model. It is proved that model cannot undergo any bifurcation about \(P_{00}(0, 0)\) and \(P_{x 0}(1, 0)\) but it undergoes an N-S bifurcation when parameters vary in a small neighborhood of \(P_{x y}^+ \left( \frac{ d}{ c} , \frac{ r \left( c - d\right)}{ b c}\right)\) by using a center manifold theorem and bifurcation theory and meanwhile, invariant close curves appears. The appearance of these curves implies that there exist a periodic or quasiperiodic oscillations between predator and prey populations. Further, theoretical results are verified numerically. Finally, the hybrid control strategy is applied to control N-S bifurcation in the discrete-time model.