Using a Dazzler system and tilting a compressor grating, we provide an effective way of using the laser group delay dispersion to continuously steer the electron beam accelerated by an asymmetric laser wakefield. The deviation angle of the electron beam was the same as that of the angularly chirped laser pulse from its initial optical axis, which is determined by the laser pulse-front-tilt (PFT). This method can be utilized to continuously control over the pointing direction of electron bunches to the requisite trajectories, especially for practical applications in highly sensitive alignment devices such as electron-positron colliders or undulators. Additionally, we investigate the effect of PFT on the properties of the electron beam.