Simulation of seismic waves is a critical component in the imaging of subsurface structures using actual data, where numerical dispersion remains a challenging task. The finite-difference (FD) approach is popular for solving wave equations because it is simple to implement and requires less memory and computing time due to recursion. However, the staggered grid finite-difference (SGFD) methods have gained popularity due to their improved accuracy and stability. In this study, we introduce an optimization approach using a genetic algorithm (GA) to minimize numerical dispersion. The SGFD coefficients were optimized to reduce numerical errors and improve the accuracy of seismic wave simulations, considering both spatial and temporal domains. Numerical simulations applied to both homogeneous and heterogeneous velocity models demonstrate that the GA-optimized SGFD schemes achieve substantial reductions in dispersion, even with lower-order approximations, when compared to other methods. An important advantage of the proposed method is that it maintains high accuracy while using lower-order approximations, which significantly reduces computational costs. For example, the optimization of 12th-order FD coefficients took approximately 20 s on a standard computer with 64 GB RAM. The findings demonstrate the efficiency of the proposed approach in improving the accuracy and stability of seismic wave simulations, providing a reliable solution for high-resolution seismic imaging.