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The structural stabilities and crystal evolution behaviors of the hyper stoichiometric compound ZrC2 (carbon rich;C/Zr>1.0) are studied under ambient and high pressure conditions using first-principles calculations in combination with the particle-swarm optimization algorithm. Six viable structures of ZrC2 in P21/c, Cmmm, Cmc21, P42/nmc, Immm and P6/mmm symmetries are identified. These structures are dynamically stable as their phonon spectra have no imaginary modes at zero pressure or at the selected high-pressure points. Among them, the P21/c phase represents the ground state structure, whereas P21/c, P42/nmc, Immm and P6/mmm phases are part of the phase transition series. The phase order and critical pressures of the phase transition are determined to be approximately 300 GPa according to the equation of states and enthalpy. Furthermore, the mechanical and electronic properties are investigated. The P21/c and Cmc21 phases display a semi-metal nature, whereas the P42/nmc, Immm, P6/mmm and Cmmm phases exhibit a metallic nature. Moreover, the present study reveals considerable information regarding the structural, mechanical and electronic properties of ZrC2, thereby providing key insights into its material properties and evaluating its behavior in practical applications.