During the self-weight penetration process of the suction foundation on the dense sand seabed, due to the shallow penetration depth, the excess seepage seawater from the outside to the inside of the foundation may cause the negative pressure penetration process failure. Increasing the self-weight penetration depth has become an important problem for the safe construction of the suction foundation. The new suction anchor foundation has been proposed, and the self-weight penetration characteristics of the traditional suction foundation and the new suction anchor foundation are studied and compared through laboratory experiments and analysis. For the above two foundation types, by considering five foundation diameters and two bottom shapes, 20 models are tested with the same penetration energy. The effects of different foundation diameters on the penetration depth, the soil plug characteristics, and the surrounding sand layer are studied. The results show that the penetration depth of the new suction foundation is smaller than that of the traditional suction foundation. With the same penetration energy, the penetration depth of the suction foundation becomes shallower as the diameter increases. The smaller the diameter of the suction foundation, the more likely it is to be fully plugged, and the smaller the height of the soil plug will be. In the stage of self-weight penetration, the impact cavity appears around the foundation, which may affect the stability of the suction foundation.