A three-dimensional computational fluid dynamics code is developed for predicting nonequilibrium flowfields over Mars entry probes. The numerical scheme is based on the cell-vertex finite volume method for a prismatic unstructured mesh system. Internal energy excitations and chemical reactions with finite rates are considered by introducing the two-temperature model of Park. Eight chemical species, C, N, O, CO, N2, NO, O2, and CO2, and nine chemical reactions are considered in the calculations. The developed code is verified in terms of prediction of heat flux to the body surface near the stagnation point of a Mars entry probe flying with the velocity of 6 km/s. The calculated heat flux reasonably agree with the calculated result in the past studies.