Zirconium carbide (ZrC) is technologically important in devices that must function at high temperatures, and its ground state is a NaCl like structure. Changes of the structure and electronic properties of ZrC under high pressure were studied within the framework of density functional theory (DFT). This research was performed for several structures, such as NaCl type (B1), CsCl type (B2), ZnS type (B3), wurtzite type (B4) and NiAs type (B8) structures for ZrC, looking for possible phase transitions induced by high pressure, and four phase transitions were found: the first is the well-known phase transition from the B1 structure to the B2 structure, which occurs at around ~291 GPa. Additionally, in the present paper we found other phase transitions: from the B8 structure to the B2 structure, from the B4 structure to the B2 structure, and lastly from the B3 structure to the B2 structure. Electronic bands are exhibited at zero pressure and temperature (with spin-orbit coupling) for the five structures. For the transition from the B1 structure to the B2 structure, bands are exhibited for two pressures, one before and the other after the transition occurs. The band structure shows that all the structures studied are metallic and nonmagnetic, with the exception the B3 structure, which exhibits a semi-metallic and nonmagnetic behaviour.