We explore the local dynamics, N‐S bifurcation, and hybrid control in a discrete‐time Lotka‐Volterra predator‐prey model in
. It is shown that
parametric values, model has two boundary equilibria:
and
, and a unique positive equilibrium point:
if
. We explored the local dynamics along with different topological classifications about equilibria:
,
, and
of the model. It is proved that model cannot undergo any bifurcation about
and
but it undergoes an N‐S bifurcation when parameters vary in a small neighborhood of
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.