We experimentally demonstrate multiple generations of high-order orbital angular momentum (OAM) modes through third-harmonic generation in a 2D nonlinear photonic crystal. Such third-harmonic generation process is achieved by cascading second-harmonic generation and sum-frequency generation using the non-collinear quasi-phase-matching technique. This technique allows multiple OAM modes with different colors to be simultaneously generated. Moreover, the OAM conservation law guarantees that the topological charge is tripled in the cascaded third-harmonic generation process. Our method is effective for obtaining multiple high-order OAM modes for optical imaging, manipulation, and communications.