Photoionization of atoms in intense, few-cycle laser pulses is inversion asymmetry. An asymmetric parameter is used to quantitatively analyze the asymmetry degree. By means of a non-perturbative quantum scattering theory and employing a three-mode laser field to mimic the short pulse, the variation of the asymmetric parameter are researched with the carrier-envelope phase and duration of the pulses. It is found that the asymmetry degree varies with the carrier-envelope phase as a sine-like pattern, and the maximum of asymmetry degree varies with pulse intensity and pulse duration. Along with the increasing laser intensities, the maximal asymmetry firstly decreases and then increases after it reaches a minimal value. At higher intensities, the asymmetry is still distinctive for relative-long few-cycle pulses. Thus, increasing the pulse intensity is helpful to observe the carrier-envelope phase-dependence.