The intensity envelopes and propagation characteristics of Lommel-Gaussian beams are investigated numerically based on gradient-index medium. The intensity expression of Lommel-Gaussian beams is provided. The zero-free region of Lommel-Gaussian beams decreases with decreasing spot of Gaussian beams, that is, the truncation effect of beams is more obvious. The spatial scale decreases with increasing half-cone angles and the hollow region of beam center increases with increasing topological charges. The spatial distribution and symmetry can be modulated by changing the asymmetric parameters. The intensity distribution of beams gradually changes from circular symmetry to axial-symmetry double-crescent pattern with increasing amplitude of asymmetric parameters and the symmetric axis of double-crescent pattern is rotated clockwise with increasing argument of asymmetric parameters. When the Lommel-Gaussian beams are propagating in a gradient-index medium, within a transmission cycle, the relative intensity distribution of beams has no change, only the beam scale has a periodic focus change. But in free space, the beam quickly evolves into two light spots. All results are helpful to study the application of Lommel-Gaussian beams.