The self-healing property of non-diffracting two-dimensional Airy beams with different parts blocked is investigated via numerical simulation. The simulation shows that the Airy beams that are partially blocked can be self-reconstructed after propagating for a certain distance. The self-healing property under the Gaussian noise perturbation is also investigated. The result shows that self-healing of the Airy beams can be realized after the beam propagates for a certain distance when the signal-to-noise ratio is appropriate. The self-healing property of Airy beams is robust, and the property can be applied in many fields such as optical tweezer system, atom trapping and manipulating, and wireless optical communications.