Carbides have attracted much attention owing to their interesting physical and chemical properties. Here, we systematically investigated global energetically stable structures of BeC2 in the pressure range of 0-100 GPa using a first-principles structural search. A transition from the ambient-pressure α-phase to the high-pressure β-phase was theoretically predicted. Chemical bonding analysis revealed that the predicted phase transition is associated with the transformation from sp(2) to sp(3) C-C hybridization. The electrical conductivity of the high-pressure phase changed from a metal (α-phase) to a narrow bandgap semiconductor (β-phase), and the β-phase had an inverted band structure with positive pressure dependence. Interestingly, the β-phase was a topological insulator with the metallic surface states protected by the time-reversal symmetry of the crystal. The results indicate that pressure modulates the electronic band structure of BeC2, which is an important finding for fundamental physics and for a wide range of potential applications in electronic devices.