We present total electron capture cross sections for collisions of N^4+ ions with atomic hydrogen in the energy range of 30-3500 eV/u calculated with the two-center atomic orbital close-coupling expansion method in a quasi-one-electron model. Various basis sets have been used to check the convergence of the calculation and the results are shown to be in general agreement with existing experimental and theoretical data. However, the small structures observed and predicted by different theories below 100 eV/u are not reproduced in the present calculation.