The propagation properties of 1+1 dimension Hermite-Gauss beam in nonlocal nonlinear lossy media are investigated by using the variational method. The laws of beam parameters followed when propagating in medium and the critical power required by forming the lossy solitons are obtained. When the initial power is close to the critical power, the beam width expands periodically and obeys the quasi-sine or quasi-cosine law. By comparison, the analytical and numerical solutions using the variational method are in good agreement with a longer distance in beam propagation.