To investigate the effect of azimuthal anisotropy on frequency-domain marine controlled-source electromagnetic (CSEM) responses, an adaptive edge-based finite-element (FE) modeling algorithm is presented in this letter. The 3-D algorithm is capable of dealing with generally anisotropic conductive media. It is implemented on unstructured tetrahedral grids, which allow for complex model geometries. The accuracy of the FE solution is controlled through adaptive mesh refinement, which is performed iteratively until the solution converges to the desired accuracy tolerance. The algorithm is validated against the quasi-analytic solutions for a 1-D layered model with anisotropy. We then simulate the marine CSEM responses over a set of 3-D anisotropic models and illustrate that the azimuthal anisotropy has a considerable influence on both the inline and broadside marine CSEM responses but to different extents.