Pressure-induced metallization and potential superconductivity of BeH2 has been a topic of interest. In the present study, we extensively explored the crystal structures of BeH2 in a wide pressure range of 0-300 GPa using an unbiased structure searching method coupled with first-principles density functional calculations. A series of pressure-induced structural transformations are predicted for BeH2, as Ibam (α phase) → P-3m1 (phase II) → R-3m (phase III) → Cmcm (phase IV). Calculated pressures of phase transition are 25, 140, and 202 GPa, respectively. The phase II is isostructural to the well-known 1T structure of transition metal dichalcogenides, which is composed of covalent bonded BeH2 slabs stacked along the perpendicular direction by van der Waals forces. The phase III is constructed by the same BeH2 slabs, but differs from the phase II in the stacking sequence. The α phase, phase II, and phase III all have insulating electronic states while their band gaps decrease as pressure increases. We predicted that BeH2 reaches a metallic state by a III → IV phase transition, instead of a direct band gap closure in phase III. The phase IV has a three-dimensional extended Be-H network formed by edge-sharing BeH8 polyhedrons with delocalized electrons. Electron-phonon coupling calculations implemented using linear response theory on the metallic BeH2 predict a large electron-phonon coupling parameter of 0.63, leading to an estimation of superconducting transition temperature (Tc) of ∼38 K at 250 GPa.