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 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.