In this paper the effect of thickness on angular-dependent magnetoresistance (MR) of La2/3Sr1/3MnO3 (LSMO) thin films grown on SrTiO3 is systematically investigated. In films thinner than 8 nm, we observe an anomalous weak peak in the MR curves when the magnetic field is parallel to the film surface. In films thicker than 10 nm, however, the weak peak disappears and a novel MR valley appears when the magnetic field is perpendicular to the film surface. The weak peak is thought to be induced by the formation of two-dimensional electron gas (2DEG) at the interface, which is confirmed by density functional theory calculations. The disappearance of the peak and appearance of the valley in the films thicker than 10 nm is associated with the formation of misfit dislocations near the interface between film and substrate, which are clearly visible in high-resolution transmission electron microscopy images. Our work could shed significant light on the influence of film thickness on 2DEG formation.