A numerical approach is established to study the hydrodynamic performance using an amphibious transport vehicle (ATV) as a research object. Numerical calculation based on the Reynolds average Navier–Stokes method is studied in terms of first layer grid height, surface meshing partition scale, and prismatic layer coefficient. Through uncertainty analysis, the correctness and convergence of the numerical approach are verified. Towing tests are conducted to compare the experimental data with the simulation results, which validated the reliability of the numerical approach under all working conditions. Results show that the numerical approach will affect the simulated results, with an average error of 3.91% for the resistance and 4.21% for the trim, meeting the requirements for analysis accuracy. Based on the proposed numerical approach, an optimization design is carried out to improve the hydrodynamic performance of the ATV. Effects of bow plate angle, stern flap angle, and stern flap install height are studied. Latin hypercube is used for sampling in optimization design, and the Kriging method is applied to establish an approximate model. The cross-validation is carried out using the leave-one-out method. Particle swarm optimization is used for parameter optimization, and the optimized configuration is verified using the numerical approach. Results indicate that the combination of bow plate and stern flap shows excellent improvement in the hydrodynamic performance of amphibious vehicles. Numerical error of the approximate model is only 0.292%, which fully verifies its accuracy and effectiveness. The optimized ATV configuration shows the best drag reduction performance of 38.81% compared to the original model.