The thorium compounds are promising candidates for the new generation nuclear fuels. Using first-principles and particle swarm optimization methods, we have explored geometrical structures and physical characteristics of thorium carbonitrides (Th2CN) in the extensive pressure range from ambient pressure to 100 GPa. At ambient pressure, we have predicted a new phase I4(1)/amd, which is energetically more favorable than the previously known phases P 4/mmm and R3m. Moreover, a series of pressure-induced phase transitions have been predicted. The thermodynamics, mechanical stabilities, elastic properties, electronic structures and chemical bonds of all these newly predicted phases have been investigated. Our predictions on the new structures at ambient and high pressures would expand the structural phase diagram of thorium carbonitrides.