Freespace selfbending of nondiffracting Airy beams was theoretically investigated with Schrodinger's equation, the factors influencing selfbending were analyzed, which were linked to actual physical quantities, and the method of acceleration control of Airy beams with gradientindex material was given. The selfbending property appearing during propagation of one and twodimensional Airy beams was numerical simulated. Moreover, the numerical simulation results that the deflection of Airy beams can be compensated and reversed with proper control. The relationship between the propagation length of compensated finite Airy beam in a gradientindex material and the decay factor was discussed. The results show that the compensated finite Airy beam can keep nondiffracting propagation when intensity of the central lobe decays from maximum to eighteen percent of the maximal value. The relationship between the propagation length of compensated finite Airy beam in a gradientindex material and the central lobe width as well as the wavelength was also studied, respectively. In practical application, three appropriate parameter values and a right gradient refractive index material can be selected through the dependent relationship between the decay factor, the central lobe width as well as wavelength and the propagation length of compensated finite Airy beam at the instance of the propagation length of compensated finite Airy beam, and optimal control of Airy beam can be realized.