We present a solution of using adaptive nodal finite-element (FE) method to solve the marine controlled-source electromagnetic (CSEM) problem for 3-D earth models in the frequency domain. The forward problem is solved based on the secondary Coulomb-gauged electromagnetic (EM) potentials. We implement an adaptive mesh refinement algorithm according to an a posteriori error estimator based on a gradient-recovery operator of the secondary EM potentials. To increase the quality of the mesh at the receiver locations, the elements containing the receiver locations are constrained by assigning them a maximum volume for the initial mesh. An unstructured tetrahedral mesh used in our approach can provide an accurate description of complex structures such as dipping layers and rough topography that are not accurately fitted using structured meshes. We first validate the adaptive FE approach and demonstrate the convergence of the adaptive grid refinement procedure using a 1-D layered model. The canonical disc model example illustrates the capability of the adaptive FE approach for 3-D CSEM modeling. The bathymetry model shows that the algorithm is well suited to deal with complex seafloor topography, which needs to be simulated exactly to avoid the misinterpretation of marine CSEM data sets.