Simulations and analyses of ultra-short ultra-intense laser propagting in plasmas with uniform and parabolic density profiles, as well as the electron injection into the wake field and the electron spectra in the stable transmission state are performed by using a particle-in-cell code. Fixing the incident laser focal spot size but changing the plasma density in a range of (0.42)1019/cm3, comparative analyses are carried out of the evolutions of the laser beam spot during the propagation of the laser pulse in the plasmas with aforementioned two density profiles, with the normalized laser intensity ranging from 1 to 6. The results show that a plasma channel with a parabolic density profile can realize a good guiding of an ultra-short ultra-intense pulse, which is beneficial for high energy electron acceleration. However, at higher densities, self-guiding can be realized by relativistic self-focusing in uniform plasma, which is conducive to simplifying the experiment and to producing more accelerated electrons.