This Letter presents for the first time a scheme to generate intense high-order optical vortices that carry orbital angular momentum in the extreme ultraviolet region based on relativistic harmonics from the surface of a solid target. In the three-dimensional particle-in-cell simulation, the high-order harmonics of the high-order vortex mode is generated in both reflected and transmitted light beams when a linearly polarized Laguerre-Gaussian laser pulse impinges on a solid foil. The azimuthal mode of the harmonics scales with its order. The intensity of the high-order vortex harmonics is close to the relativistic region, with the pulse duration down to attosecond scale. The obtained intense vortex beam possesses the combined properties of fine transversal structure due to the high-order mode and the fine longitudinal structure due to the short wavelength of the high-order harmonics. In addition to the application in high-resolution detection in both spatial and temporal scales, it also presents new opportunities in the intense vortex required fields, such as the inner shell ionization process and high energy twisted photons generation by Thomson scattering of such an intense vortex beam off relativistic electrons. Light beams can exhibit helical wave fronts: the light phase "winds up" around the spatial beam center and forms an optical vortex. The phase wind imprints an orbital angular momentum (OAM) to the beam [1,2]. The characteristic helical phase profiles of optical vortices are described by expðilϕÞ multipliers, where ϕ is the azimuthal coordinate and the integer number l is their topological charge, corresponding to the order of the mode. The total phase accumulated in one full annular loop is 2πl, and an OAM of lℏ is carried by per photon for an l-order linearly polarized optical vortex beam. Based on this, the high-order optical vortex beam provides a powerful tool in optical information to investigate the entanglement state [3] and for studies of cold atoms and enhancing atomic transition [4][5][6][7].In order to provide more quantum information and for other potential applications, high-order vortex beams are required. However, limited by the etching resolution, the common method using forked diffraction grating [8] or the spiral phase plates [1] to generate the optical vortex beams is difficult to be used to obtain them. Many studies have attempted to generate light beams with OAM. For example, a relativistic electron beam can act as a mode converter that interacts with a laser in a helical undulator [9-11] and high-energy photons in MeV-GeV with OAM can be obtained by Compton backscattering of twisted laser photons off relativistic electrons [12], where the mode of the Laguerre-Gaussian (LG) pulse remains unchanged. In addition, in view of the gas high-order harmonics generation (HHG) scheme [13][14][15], because of the confluence of OAM and HHG, this scheme has an extraordinarily promising perspective. The observed harmonics possess a helical wave front in both experimental [16,17] and theoretical...