The propagation properties of two orthogonal polarized center-coincidence Hermite-Gaussian (HG) beams were investigated in strongly nonlocal medium with exponential-decay response using variational method. The evolutional equations for the parameters of HG beams and one critical power Pc were obtained. The HG spatial optical solitons come into being when the two incidental powers are both equal to the critical power. However, when two beams are incident with total power 2Pc while the two incident powers are not equal, they form HG breathers. By means of numerical simulation, the beam with low order may have approximate soliton solution. When the orders of beam are higher than the third, there are no soliton solutions. By comparing variational solution with numerical solution, it’s found that when the order of beams are under the third the variational solutions can well reveal the propagation properties of orthogonal polarization center-coincidence double HG beams in strongly nonlocal medium with exponential-decay response.