The fish anchor is an economically viable offshore foundation engineering technology that has been proposed in recent years. By fish anchor, we mean a fish-shaped dynamically installed anchor that can penetrate into the seabed through water by its own weight. However, the existing research studies seldom consider the hydrodynamic characteristics of its free fall installation, resulting in uncertainties regarding its underwater installation characteristics. Therefore, based on OpenFOAM, this study first investigated the directional stability of fish anchors during its underwater falling process through the static model analysis method and dynamic model analysis method. The findings indicated that the directional stability of fish anchors was insufficient, rendering them suitable only for release and installation at low heights (i.e., less than 4.2 times the anchor length) without marine environmental loads. Furthermore, the anchor inclination angle during installation is significant, thereby impacting its penetration depth and pull-out capacity in the seabed. To solve this problem, the concept of an innovative booster-assisted fish anchor is proposed, which can significantly enhance the directional stability of conventional fish anchors. Results show that the maximum installation height of the new booster-assisted fish anchor is increased by 2.4 times compared to the original design, thereby enhancing both the penetration speed and uplift capacity. Based on the findings, recommended installation and construction conditions are provided. Finally, a predictive formula for the installation height and verticality of the new booster-assisted fish anchor under current action is presented to offer guidance for engineering applications.