Generation of higher-order Laguerre-Gaussian(LG) beams (vortex beams) and higher-order Hermite-Gaussian(HG) beams directly from the laser was theoretically and experimentally studied. The intensity distribution characteristics of higher-order LG beams and higher-order HG beams were theoretically studied, and the numerical simulation results were given. The Pr:YLF crystal was end-pumped by a 445 nm blue semiconductor laser, under certain conditions, the higher-order LG beam and the higher-order HG beam of wavelength 640 nm was directly delivered from the plano-concave laser cavity. The experimental results show that the higher-order LG beams and the higher-order HG beams from the laser cavity are in agreement with the theoretical simulation. It is shown that the device for generating the higher-order modes is simple. The results of this paper seems very important for generation of higher-order laser beams and their applications.