The thermodynamic properties of a q-generalized ideal boson system with the general energy spectrum ε=aps in a D-dimensional space are investigated, based on the q-generalized statistical distributive function derived by Tsallis entropy. Several important parameters of the system such as the critical temperature tha Bose-Einstein condensation (BEC) occurs, the specifie heat at constant volume, etx. are derived analytically. It is found that the conditions that BEC may occur and the continuity of the specific heat at critical temperature are the same as those of an ordinary boson system. However, the thernodynamic properties of a q-generalized ideal boson system are closely depend on q and D/s and consequently there are some novel results.