Using Monte Carlo simulations, we investigate the structural characteristics of an interacting hard-sphere system with shifted charge to elucidate the effect of the noncentrosymmetric interaction on its phase behavior. Two different phase transitions are identified for this model system. With increasing volume fraction, an abrupt liquid-to-crystal transition first occurs at a significantly lower volume fraction than in centrosymmetrically charged systems. This is due to the stronger effective interparticle repulsion caused by the additional charge anisotropy. Moreover, within the crystal state at higher volume fraction, the system further undergoes a continuous disorder-to-order transition with respect to charge orientation. Detailed analyses in this work disclose the nature of these transitions, and orientation fluctuation can cause noncentrosymmetric unit cells. The dependence of crystal formation and orientational ordering on temperature was also examined. These findings indicate that the noncentrosymmetric interaction in this work results in additional freedoms to fine-tune the phase diagram and increase the functionalities of materials. Moreover, these model studies are essential to advance the future understanding regarding the fundamental physiochemical properties of novel Janus colloidal particles and protein crystallization conditions.