We propose and numerically analyze the transverse acceleration control for the Airy-like beams from incomplete Airy waveguide and Airy waveguide by rainbow effect. We show that the Airy-like beams have an obvious change in transverse acceleration with a slight variation (10 nm) in incident wavelength. The rainbow phenomenon is introduced to study the Airy-like beam propagation with a different wavelength. The equivalent initial launch angle is also considered to explain transverse acceleration of the Airy-like beams.