Using the Dirac–Heisenberg–Wigner formalism, effects of the asymmetric pulse shape on the generation of electron-positron pairs in three typical polarized fields, i.e., linear, middle elliptical and circular fields, are investigated. Two kinds of asymmetries for the falling pulse length, short and elongated, are studied. We find that the interference effect disappears with the shorter pulse length and that the peak value of the momentum spectrum is concentrated in the center of the momentum space. In the case of the extending falling pulse length, a multiring structure without interference appears in the momentum spectrum. Research results show that the momentum spectrum is very sensitive to the asymmetry of the pulse as well as to the polarization of the fields. We also find that the number density of electron-positron pairs under different polarizations is sensitive to the asymmetry of the electric field. For the short falling pulse, the number density can be significantly enhanced by over two orders of magnitude. These results could be useful in planning high-power and/or high-intensity laser experiments.