The marine controlled-source electromagnetic (CSEM) method offers a range of applications in marine geophysics, including mapping hydrocarbon reservoirs, studying seafloor geology, identifying potential mineral deposits, and investigating hydrate occurrences. Nevertheless, the interpretation of marine CSEM data becomes challenging when complex anisotropy is present. Therefore, we extend the scope of numerical simulations of 3-D marine CSEM responses from a specific case of dipping anisotropy to general anisiotropy based on a goal-oriented adaptive finite element (FE) method. We verify the upgraded argorithm using a 1-D anisotropic layered model with quasi-analytical solutions, and then apply the algorithm to compute marine CSEM responses over a set of 3-D anisotropic models. The behavior of the responses is explained by visualizing the flow of electromagnetic energy within the anisotropic conductivity structures using the Poynting vector, which helps explain how the energy propagates and interacts with the anisotropic media, providing insights into the observed response patterns. The numerical results clearly demonstrate that both the dipping and azimuthal anisotropy in the sediment have considerable impacts on marine CSEM responses, but their effects follow different patterns and highly dependent on the orientation of the electric dipole source utilized. However, the influence of the anisotropic reservoir can hardly be observed. This study emphasizes the significance of incorporating anisotropy into the interpretation of marine CSEM surveys. It contributes to the understanding of the impacts of general anisotropy on marine CSEM responses and provides a valuable approach for accurately modeling and interpreting marine CSEM data in the presence of anisotropic conductivity.