A model of the martian exosphere is built for average solar conditions. A Chamberlain's approach (Chamberlain, 1963) is used to describe the O, CO, CO2, and O2 thermal exospheric components. The average thermal oxygen density at 300 km in altitude varies by about one order of magnitude with seasons. A Monte-Carlo test particle simulation is also developed in order to estimate the non-thermal oxygen component of the exosphere. The seasonal variation of the non-thermal oxygen average density is much less than the thermal component but displays clear seasonal variations of its spatial distribution. The neutral oxygen atomic escaping flux varies from 2.9 to 5.3 ×1025 s-1 in good agreement with Valeille et al. (2009). Mars's oxygen exosphere is thermal below 600 km and non-thermal above 700 km at all seasons. The typical scale height is ∼45 km for thermal O and ∼500km for the non-thermal oxygen density. The total photoionization rate above 300 km corresponds to a CO2+/O+ total production ratio between 0.004 and 0.02. When compared to the composition of the escaping flux measured by ASPERA-3/Mars Express, this suggests that ions formed below 300km should significantly contribute to the escaping ion flux and/or that a significant part of the newly O+ ions reimpacts Mars. The simulated oxygen density profile is also compared to the recent observed profile by Alice/Rosetta (Feldman et al., 2011). Although the scale height of our simulated non-thermal oxygen exosphere and the transition from thermal to non-thermal dominated exospheres are slightly higher than suggested by Feldmann et al. (2011), a good agreement is found when taking into account the uncertainties of ALICE/ROSETTA observations.