We simulate the phase transition processes of aligned crystalline boron nitride (BN) nanotube bundles under transverse pressure, and investigate the phase transition mechanism and transition conditions. The antiparallel polar bonds rule, associated with the interaction between the tubes, is demonstrated to be crucial to such phase transitions. And the curvature of the tubes can greatly affect the phase transition behavior. We discover a unique sp(2)-sp(3_)sp(2) transition and series of new BN crystal phases including a novel porous sheet-stacking-up form with the lightest density (2.01 g/cm(3)), which could be used in highly efficient energy storage.