The photoionization of H atoms irradiated by few-cycle laser pulses is studied numerically. The variations ofthe total ionization, the partial ionizations in opposite directions, and the corresponding asymmetry with thecarrier-envelope phase in several pulse durations are obtained. We find that besides a stronger modulation onthe partial ionizations, the change of pulse duration leads to a shift along carrier-envelope (CE) phase in thecalculated signals. The phase shift arises from the nonlinear property of ionization and relates closely to theCoulomb attraction of the parent ion to the ionized electron. Our calculations show good agreement with theexperimental observation under similar conditions.