  Polarized electron beam production via laser wakefield acceleration in
pre-polarized plasma is investigated by particle-in-cell simulations. The
evolution of the electron beam polarization is studied based on the
Thomas-Bargmann-Michel-Telegdi equation for the transverse and longitudinal
self-injection, and the depolarization process is found to be influenced by the
injection schemes. In the case of transverse self-injection as found typically
in the bubble regime, the spin precession of the accelerated electrons is
mainly influenced by the wakefield. However, in the case of longitudinal
injection in the quasi-one-dimensional regime (for example, F. Y. Li \emph{et
al}., Phys. Rev. Lett. 110, 135002 (2013)), the direction of electron spin
oscillates in the laser filed. Since the electrons move around the laser axis,
the net influence of the laser field is nearly zero and the contribution of the
wakefield can be ignored. Finally, an ultra-short electron beam with
polarization of $99\%$ can be obtained using longitudinal self-injection.
