Plasma wakefield acceleration driven by ultra short ultra intense laser pulse interacting with gas target has been studied for almost four decades. Monoenergetic electron beams with central energy of multi-giga electron-volt have been achieved in a centimeter-scale acceleration distance. Currently, the highest energy of electrons accelerated by laser wakefield is 8 GeV. In order to further improve the quality of such electrons, many kinds of electron injection schemes have been proposed such as density gradient injection, colliding pulse injection and ionization injection. Electrons under the suitable conditions can be trapped by the strong plasma wakefield. Those trapped electrons are then accelerated in the wakefield. In a nonlinear regime, the wakefield shows a “bubble” structure. Electrons with transverse momentum can oscillate in the wakefield and produce considerably betatron radiation in the ultraviolet and X-ray region. In this paper, we study the electron injection around the sharp plasma-vacuum boundary. The effects of the slant angle of the boundary on the final electron quality are investigated in detail. Our results show that with optimal slant density transition around the vacuum plasma boundary, both the beam quality and the injection charge in the second “bubble” can be improved. Two-dimensional particle-in-cell simulations show that the injection charge in the second wake bucket can be increased three times when an optimal slant angle is used compared with a vertical boundary. The driving pulse’s polarization also affects the injection charge. When the polarization is in the injection plane the injection charge in the first bucket can be triply increased compared with the case when the polarization is out of the plane. The reasons for the enhanced injection charge and transverse oscillation are found by tracing the initial injection positions and trajectories of the electrons. These studies would benefit the electron acceleration and its applications, such as compact betatron radiation source.