Above-threshold ionization (ATI) is one of the most fundamental processess when atoms or molecules are subjected to intense laser fields. Analysis of ATI process in intense laser fields by a Wigner-distribution-like (WDL) function is reviewed in this paper. The WDL function is used to obtain various time-related distributions, such as time-energy distribution, ionization time distribution, and time-emission angle distribution and so on, of atoms in laser field pulses with different laser parameters. For the linearly polarized laser pulses, the time-energy distribution intuitively shows from a quantum point of view the relationship between the ionization moment and the final energy and clearly reveals the origin of interference structures in the photoelectron spectrum. In particular, for linearly polarized few-cycle laser pulses, all calculated distributions show the dependence of electron behavior on the ionization time, emission direction, and carrier-envelope phase (CEP). For elliptically polarized few-cycle pulses, we calculate the angular distribution, ionization time distribution, and time-emission distribution, which are compared with the semiclassical calculations. Analysis shows that the offset angle (difference between positions of the peaks in the angular distributions obtained by two methods) in the angular distributions does not correspond to the offset time (difference between positions of the peaks in the ionization time distributions obtained by two methods) in the ionization time distributions, which implies that the attosecond angular streaking technique based on this correspondence between the offset angle and time is in principle inaccurate. Furthermore, the offset time cannot be interpreted as tunneling time.