A novel method for generating high-order Laguerre-Gaussian beams is explored in this work. The astigmatic Gaussian beams are experimentally investigated by a hemi-cylindrical laser cavity. Based on the experimental laser beam profile, the equivalent radius of curvature induced by the thermal lens effect for the hemi-cylindrical cavity can be evaluated. A cylindrical lens is mounted outside the cavity with a rotated angle to provide an astigmatic compensation for the astigmatic Gaussian beam. The lasing beam of astigmatic high-order Hermite-Gaussian mode can be transformed into a high-order Laguerre-Gaussian beam.