Taking the rigid NACA0012 airfoil as the object, the key structural parameters of the spring–mass system that govern the dynamics of the double-elastic-constrained flapping hydrofoil are numerically studied in this paper. A two-dimensional numerical model, based on the CFD software FINE/Marine, is established to investigate the influence of the spring stiffness coefficient, frequency ratio, and damping coefficient on the motion and performance of the flapping hydrofoil. This study demonstrates that when the structural parameters are adequately adjusted, the power factor exceeding 1.0 has been achieved, and the corresponding efficiency is up to 37.8%. Moreover, this system can start and work within a wide range of damping coefficients. However, the hydraulic efficiency and power coefficient are sensitive to the change in damping coefficient, so it is very necessary to design an appropriate power output. Lastly, the most obvious parameter affecting the energy acquisition performance is the spring stiffness coefficients. Frequency ratios in the two directions have little influence on the peak value of the power coefficient, but they will cause the change of damping coefficients of the peak point. The key structural parameters studied in this paper provide a useful guideline for an optimized design of this interesting system through searching for the best performance.