In this paper, an ultra-low profile anisotropic holographic metasurface is proposed to generate a linearly polarized high-order Bessel vortex beam carrying orbital angular momentum with predesigned topological charge. Based on the leaky-wave theory and optical holographic principle, the anisotropic impedance pattern can be properly mapped by shaping the quasi-periodic metasurface with different meta-atom sizes. Compared with the prevalent spatial wave-modulated metasurface, this surface wave-modulated holographic metasurface effectively transforms a reference wave excited by a feeding source in a single point at the center of the antenna to a leaky high-order Bessel vortex beam without any extra air feeding, which enables a unique characteristic of error-free alignment between the air feeding and designed metasurface. The good agreement between the numerical simulation and the measured result demonstrates that the proposed approach can be employed to launch a linearly polarized high-order Bessel vortex beam with an arbitrary topological mode of interest.