In this paper, we propose that both the quasi-transverse-magnetic (TM) and quasi-transverse-electric (TE) Airy plasmons can be supported in graphene-based waveguides. The solution of Airy plasmons is calculated analytically and the existence of Airy plasmons is studied under the paraxial approximation. Due to the tunability of the chemical potential of graphene, the self-accelerating behavior of quasi-TM Airy plasmons can be steered effectively, especially in multilayer graphene based waveguides. Besides the metals, graphene provides an additional platform to investigate the propagation of Airy plasmons and to design various plasmonic devices.