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A computational model of high-current pulsed arc discharge in air is proposed. This is, in general, a 2D model which takes into account the gas dynamics of the discharge channel, real air thermodynamics in a wide range of pressures and temperatures, the electrodynamics of the discharge including the pinch effect, and radiation. The 1D version of the model is tested and verified on several numerical and experimental works reported recently. It is concluded that low and moderate current discharges are satisfactorily described with the model. The model was then applied to simulate the electric discharge in air for the currents 1–250 kA and characteristic rise times in 13–25 µs, and the results of the calculations were compared with experimental ones. It was concluded that most characteristics of the discharge are predicted well. Namely, the arc column radius and shock wave position agree well with experimental data for all the current amplitudes and rise times considered. Radial distributions of temperature and electron density also satisfactorily agree with experimental data. It was found that the pinch effect should be considered for currents higher than 100 kA.