A decentered high-elliptical Gaussian beam(DHEGB) was defined by a tensor method.Its propagation formula passing through an axially nonsymmetrical paraxial optical system was derived by vector integration.The formula can be reduced to the one for a decentered elliptical Gaussian beam under certain condition.Using the formula,propagation characteristics of the DHEGB in free space were calculated and discussed.The results show that the beam spot of the DHEGB rotates with propagation distance,and the propagation property is closely related to the decentered parameter.