This study develops a high-precision numerical simulation method that considers free surface deformation to analyze fluid dynamics in dolphin kick swimming. We integrate an interface tracking method with the Moving Computational Domain (MCD) method and the unstructured moving-grid finite-volume method. The simulation validation demonstrates agreement with theoretical solutions, confirming the method′s accuracy in analyzing flow fields with free surfaces. Using this approach, we analyze flow fields around dolphin kick swimmers and evaluate how gravity and free surface deformation affect propulsion and drag forces. The results indicate that the free surface experiences an upward displacement in front of the swimmer, a downward displacement above the back, and wave formation in the wake. Comparative analyses indicate that pressure distribution variations caused by gravity and vortex structures significantly influence propulsion and drag. Through simulations with varied joint angles and kick frequencies, we establish that swimming speed increases linearly with both joint angle amplification and stroke period reduction. Our analysis shows a proportional relationship between swimming velocity and the combined effect of increased joint angles and decreased kick cycle times. Our findings validate the effectiveness of the proposed simulation technique for determining optimal joint angles and stroke periods to achieve efficient swimming speeds in competitive dolphin kick swimming.