We propose a comprehensive theory to analyze the Goos-Hänchen (GH) shift for an arbitrarily polarized Airyprime beam reflected at the air-dielectric interface. We derive general expressions for the spatial and angular GH shifts and establish a close relationship between the GH shift of the Airyprime beam and the GH shift of the Airy beam. We also predict the novel optical effects of a significantly enhanced spatial GH shift and an almost disappeared angular GH shift when the horizontally polarized Airyprime beam is reflected near Brewster's angle.