Elastic neutron scattering experiments have been carried out in order to reveal the magnetic structure and 5f electronic state of NpRhGa5. This material exhibits two successive antiferromagnetic transition at TN1 = 36 K and TN2 = 33 K, respectively. A-type antiferromagnetic structure with the propagation vector q = [0, 0, 1/2] has been revealed below TN1. This antiferromagnetic structure is the same as that for NpCoGa5, UPdGa5 and UPtGa5. The identical magnetic structure is reasonably understood from the electronic structure; These iso-electronic compounds have very similar cylindrical fermi surfaces. We found a remarkable change in the moment direction, namely the Np moment is parallel and perpendicular to the c-axis for TN2 < T < TN1 and T < TN2, respectively. The magnetic moment exhibits a remarkable jump at TN2, indicating that the moment reorientation is associated with the transition of 5f electronic state at TN2. This electronic transition would be a consequence of the competition of the magnetic and/or quadrupolar interaction between different 5f electronic states. The observed magnetic form factor indicates the dominant contribution of the orbital moment, while the orbital contribution is reduced from the Np3+ free ion state. This is consistent with the itinerant character of the 5f electrons in NpRhGa5, which is revealed by the dHvA experiments and the band calculation study.