Magnesium borohydride (Mg(BH4)2) is one of the potential hydrogen storage materials. Recently, two experiments [Y. Filinchuk, B. Richter, T. R. Jensen, V. Dmitriev, D. Chernyshov, and H. Hagemann, Angew. Chem., Int. Ed. 50, 11162 (2011); L. George, V. Drozd, and S. K. Saxena, J. Phys. Chem. C 113, 486 (2009)] found that α-Mg(BH4)2 can irreversibly be transformed to an ultra dense δ-Mg(BH4)2 under high pressure. Its volumetric hydrogen content at ambient pressure (147 g/cm(3)) exceeds twice of DOE's (U.S. Department of Energy) target (70 g/cm(3)) and that of α-Mg(BH4)2 (117 g/cm(3)) by 20%. In this study, the experimentally proposed P4(2)nm structure of δ-phase has been found to be dynamically unstable. A new Fddd structure has been reported as a good candidate of δ-phase instead. Its enthalpy from 0 to 12 GPa is much lower than P4(2)nm structure and the simulated X-ray diffraction spectrum is in satisfied agreement with previous experiments. In addition, the previously proposed P-3m1 structure, which is denser than Fddd, is found to be a candidate of ε-phase due to the agreement of Raman shifts.