The complex variable Hermite-Gaussian beams with different orders have different intensity and phase distributions. When the order increases, the number of vortex singularities increases, i.e., the number is equal to the order, and both the beam width andellipticity also increase. The split-step Fourier method is used to numerically simulate the propagation of complex variable Hermite-Gaussian beams in strong nonlocal medium. It is found that when the initial power of the beam is not equal to the critical power, breather with oscillatory width can be obtained. When the initial power of the beam is equal to the critical power, the stable soliton can be obtained. Further study shows that the rotation direction of the soliton light intensity depends on the sign in front of the imaginary part in the parameter ξ, and the critical powers of solitons with different orders are equal, but the orbital angular momentum increases with increase of the order. Moreover, after adding noise, the propagations of complex variable Hermite-Gaussian solitons are still stable.