Abstract: Vacuum laser acceleration (VLA) has the advantages of large gradient of acceleration field and large charge of collimated electrons. For certain topics, the production of electrons with initial velocity and the injection of these electrons in vacuum are main problems restricting the development of VLA. A new vacuum laser acceleration scheme is proposed in this paper, in which an ultra-short ultra-intense laser pulse is grazing incident into a cone target.Two-dimensional particle-in-cell simulation is used to confirm this acceleration scheme, which can produce collimated GeV-class electron beams in millimeters. The intense laser pulse is a linearly y-polarized laser with intensity of 10²¹ W/cm². The effect of radius of the target is studied in this paper.