A new statistical distribution of a q-deformed boson gas derived by Tuszynski et al. is used to investigate the thermodynamic properties of a q-deformed ideal Bose gas with the general energy spectrum in a D-dimensional space. The problems relative to Bose-Einstein condensation (BEC) of the q-boson system are discussed. It is found that at high temperatures, the generalized Bose integral for a given q-boson system does not vary with q, while the different values of q only affect the generalized fugacity of the q-boson system. Moreover, it is expounded that the conditions that BEC occurs and the relevant condensation characteristics are closely dependent on the values of q.