We describe a three-dimensional (3D) finite-element oceanmodel designed for investigating the large-scale oceancirculation on time scales from years to decades. The modelsolves the primitive equations in the dynamical part andthe advection-diffusion equations for temperature andsalinity in the thermodynamical part. The time-stepping isimplicit. The 3D mesh is composed of tetrahedra and hasa variable resolution. It is based on an unstructuredtwo-dimensional surface mesh and is stratified in thevertical direction. The model uses linear functions forhorizontal velocity and tracers on tetrahedra, and forsurface elevation on surface triangles. The verticalvelocity field is element-wise constant. An importantingredient of the model is the Galerkin least-squaresstabilization used to minimize effects of unresolvedboundary layers and make the matrices to be inverted intime-stepping better conditioned. The model performance wastested in a 16-year simulation of the North Atlantic usinga mesh covering the area between 7 N and 80 N andproviding variable horizontal resolution from 1/3 to1.5 degrees.