Multi-vortex-Gaussian beams with different numbers of vortices and topological charges have different light intensity and different phase distribution. When the number of vortices increases, the number of vortex singularities increases and the statistical beam width also increases. The propagation of multi-vortex-Gaussian beams in a non-local medium with negative refractive index is numerically simulated by the split-step Fourier method. It is found that the asymmetry of the vortex point about the origin or the unequal topological charges of each vortex point can result in the change of the transmission direction of the soliton, so the transmission direction of the beam can be controlled by changing the position of the vortex point and the number of topological charges. If the sign in front of the imaginary part of the vortex point changes, the rotation direction of the soliton will change. In addition, the critical power and orbital angular momentum of the soliton will increase with the increase of the topological charge. Therefore, the beam information can be encoded by the vortex point position, the number of vortex points, and the topological charge, so that the beam can carry more information when it is transmitted in the medium.