With their intriguing diffraction-free, self-accelerating, and self-healing properties, Airy plasmons show promise for use in the trapping, transporting, and sorting of micro-objects, imaging, and chip scale signal processing. However, high dissipative loss and lack of dynamical steerability restrict the implementation of Airy plasmons in these applications. Here we reveal hybrid Airy plasmons for the first time by taking a hybrid graphene-based plasmonic waveguide in the terahertz (THz) domain as an example. Due to coupling between optical modes and plasmonic modes, the hybrid Airy plasmons can have large propagation lengths and effective transverse deflections, where the transverse waveguide confinements are governed by the hybrid modes with moderate quality factors. Meanwhile, the propagation trajectories of the hybrid Airy plasmons are dynamically steerable by changing the chemical potential of graphene. These hybrid Airy plasmons may promote the further discovery of non-diffracting beams along with the emerging developments of optical tweezers and tractor beams.