In this paper，the Laguerre-Gaussian vortex beam is decomposed into multiple Hermite-Gaussian sub beams based on the interconversion relationship between the Laguerre-Gaussian and Hermite-Gaussian modes，and the intensity distribution of the mode conversion relationship is given. Then，using the Huygens-Fresnel principle，an expression for the field distribution at the receiving surface of multiple Hermite-Gaussian sub beams propagated in vacuum under non-parallelaxis conditions is derived. The intensity and phase distributions of multiple Hermite-Gaussian sub beams with different topological charges and distances during vacuum transmission are investigated using numerical analysis. The results show that the multiple Hermite-Gaussian sub beams have a high light intensity energy concentration in the main fan-site region in the short distance and it can be used for precise optical manipulation. The isophase line of the sub beams field changes from a straight line to a smooth arc as the propagation distance increases. For long-distance propagation，the phase variation of the non-parallel-axis approximation multiple Hermite-Gaussian sub beams is much smaller than the phase distribution of the parallel-axis approximation Laguerre-Gaussian beam. It can be seen that the non-parallel-axis approximation condition of the multiple Hermite-Gaussian sub beams is more suitable for long-distance transmission. The results in this paper can provide a theoretical basis for the propagation of Laguerre-Gaussian vortex beams with high topological charge and wide divergence angle.