Inverted polarity effect was studied at the breakdown of point-to-plane discharge gap filled with air at a pressure range of 0.013-0.3 MPa. High-voltage nanosecond pulses were applied to the electrode with a small radius of curvature. Pulser was operated at both negative and positive polarities in the single-pulse mode. Waveforms of voltage pulse, discharge current, and intensity of the discharge plasma radiation near the electrode with a small radius of curvature were registered. It was obtained that at the breakdown of point-to-plane discharge gap filled with air, the breakdown voltage at positive polarity of the pointed electrode was higher than that at negative one. The inverted polarity effect was shown to come to naught with an increasing of air pressure up to 0.3 MPa. It is suggested that the inverted polarity effect is related to the impeded formation of the explosive emission centers on the flat electrode (cathode) after arrival of the ionization wave front to the one. In addition, both the inverted and the ordinary polarity effects were not observed at the breakdown of nitrogen at pressures of 0.4 and 0.7 MPa.