the generation of Airy beams, it is highly desirable to locally control the amplitude and phase of the output beam simultaneously so as to satisfy the polynary amplitude and binary phase distributions. Traditional methods to generate an Airy beam usually require a complex and bulky optical system, such as a Fourier transform (FT) lens and a spatial light modulator, [3,6] or an FT lens and an FT plane, [7] which is against a high-density optical integration on a chip.Metamaterials and their 2D versions, metasurfaces, have provided an unprecedented approach to locally manipulate the phase, [10,11] amplitude, [12,13] and/ or polarization [14] of the electromagnetic (EM) waves. Recent studies have demonstrated that, manipulating the amplitude and phase simultaneously and independently leads to new wavefront manipulation effects and applications. [15][16][17] Inspired by the flexibility of introducing complex field distributions, [18] various Airy beam generators, either for free-space light, [19][20][21][22][23][24][25] or surface plasmons, [20,[26][27][28][29][30] have been proposed and demonstrated based on metasurfaces. Different from the metasurface lenses or holograms that merely require phase modulation, controlling both the amplitude and phase simultaneously is highly required to generate high-quality Airy beams that are capable of keeping good nondiffracting nature and stable full width half-maximum (FWHM) during propagation. [23] Typically, wavelength-scale engineered gratings, [26,29] graded nanocavity array, [27,28] and nanoslit resonators [20,30] are widely used to generate plasmonic Airy plasmons. In parallel with the above advances, free-space Airy beams, have been successfully realized by using dielectric nanofins, [21] metal nanorods, [23] and C-shaped apertures. [19,22,24,25] All these meta-atoms provide us with a robust tool to control the wave front of output beams appreciably across a resonance, and hence can be utilized to generate Airy beams. Since the building blocks of these metasurfaces are typically some resonant structures so that the amplitude and phase cannot be kept to satisfy an Airy function at frequencies out of the resonance frequency, such schemes thus exhibit limited working bandwidths around the resonance frequency. While promising steps have been taken to broaden the working bandwidth with proper design of C-aperture metasurface, and the working bandwidth of the Airy beams can be somewhat expanded around the resonance frequency, [22,24] the transmission efficiencies are typically lowThe Airy beam has attracted considerable research interest owing to the intriguing diffraction-free, self-accelerating, and self-healing properties, and hence has found numerous applications in photonics. Metasurfaces provide a compact method to generate Airy beams, but the available Airy beam generators suffer from the issue of narrow bandwidth since they typically rely on resonance principles. Here, hyperbolic metamaterials (HMMs) are proposed to address this issue by taking advantage of the broadba...