This study investigates the stability and bifurcation analysis of a discrete-time predator-prey system using a nonstandard finite difference scheme. We analytically demonstrate that the system undergoes a Neimark–Sacker bifurcation near its unique positive fixed point. To suppress the resulting chaotic dynamics, control strategies based on the OGY and state feedback control methods are implemented. Numerical simulations are conducted to support the theoretical analysis, confirming the effectiveness of the proposed control techniques.