The electronic structure and magnetic properties of NpCoGa5 are investigated in the framework of relativistic density functional theory in the local spin density approximation (LSDA) with and without orbital polarization (OP) corrections. A detailed analysis of the Fermi surface is presented. Comparison of the calculated angular dependence of the de Haas-van Alphen frequencies with recent experimental data shows that LSDA reproduces the main features of the Fermi surface topology, while the spin and orbital moments of NpCoGa5 are less well described. The inclusion of OP corrections leads to a very good agreement between calculated and measured de Haas-van Alphen frequencies, but does not yield a significant improvement of the calculated magnetic properties. We predict that NpCoGa5 shows an intrinsic GMR effect at moderate magnetic field.