The energetic neutral atom (ENA) distribution around Mars is characterized by ENAs which have their origin in the solar wind (HSWENA) and by a second particle population which comes from the planetary atmosphere (HplENA). Since planetary energetic neutral hydrogen atoms contain information about the Martian water inventory, we calculated their flux and energy distribution. We used a test particle model which involves the motion in the external electric and magnetic field. It is shown that after a planetary neutral hydrogen atom is transformed into an ion via charge exchange with solar wind particles, solar UV, or electron impact, it is accelerated to higher energies by the convective electric field and gradually guided by the solar wind plasma flow around the planetary obstacle. Some of the newly born planetary ions take part in a charge exchange reaction with particles of the upper Martian atmosphere and will thus be transformed into planetary ENAs. The integral flux of planetary hydrogen ENAs is found to be highest in the magnetosheath with a distinct asymmetry between the direction of the solar wind magnetic and the solar wind electric field. For typical solar wind parameters the maximum planetary ENA flux can reach almost 10% of the unperturbed solar wind flux at solar minimum in some beams generated at middle latitudes in the dayside magnetosphere. The energy of planetary ENAs upstream of the bow shock can exceed the solar wind energy, while the downtail magnetosheath region is populated by ENAs with energies below that of ENAs originating from the solar wind. Our results suggest that the ENA detector on board of the Mars Express spacecraft can separate the hydrogen ENA populations from the solar wind ENAs by a careful analysis of the particle energies.