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Based on the angular spectrum decomposition and partial-wave series expansion methods, we investigate the radiation force functions of two Airy–Gaussian (AiG) beams on a cylindrical particle and the motion trajectory of the particle. The simulations show that the particle can be pulled or propelled into either the positive or negative transverse direction by tuing the phase difference between the two AiG beams appropriately; and the larger the beam widths of the two AiG beams are, the bigger the radiation force can be obtained to control the particle. In addition, the direction of the accelerated particle can be controlled while the dimensionless frequency bandwidth changes. The results indicate that the phase plays an important role in controlling the direction of the particle, which may provide a theoretical basis for the design of acoustical tweezers and the development of drug delivery.