The theoretical model of the evaporation and condensation heat transfer process of the axially grooved heat pipe (AGHP) assisted by gravity under small angle inclination is established to investigate the evaporation regimes and the heat transfer characteristics of AGHP. To reveal the heat transfer mechanism of the AGHP, the working state and gas-liquid interface distribution of the AGHP with different input power are analysed. And the influence of the inclination angle and groove structure (length-width ratio), including on the maximum heat transfer of AGHP is also discussed. The numerical simulations indicate that: With the increasing input power, the fin-film evaporation regime transits to the corner-film evaporation regime in the AGHP. The growing inclination angle enhances the gravitational effect on the liquid reflux and increases the critical input power for the evaporation regime transition. As the aspect ratio of the grooves increase, the increasing maximum radius of the meniscus leads to stronger heat transfer capacity of the AGHP.