It is difficult to use the conventional method to obtain accurate analytical solution of the Schrodinger equation in the nonlocal nonlinear media. The propagation of Hermite-Gaussian (HG) beams in the strongly nonlocal nonolinear media is discussed with a variational method in this paper. The nonlinear Schrodinger equation can be simplified through expanding the response function in the nonlinear medium. The solution of high-order Gaussian beam soliton is obtained. The beam width of HG beam is unchanged when it propagates in the media by using numerical simulations. The results show that the analytical solution is closer to the numerical solution when the degree of the nonlocality is very large.