This paper presents a highly efficient Airy beam generator at microwave frequency using a transparent metasurface with a receiving-transmitting scheme. The amplitude and phase of the transmitted orthogonal polarization wave can be flexibly controlled by orientation angles of receiving and transmitting patches of the proposed meta-atom. Utilizing this property to reshape the field of transmitted waves following the desired phase and amplitude profile of the Airy wave packet, an Airy beam generator is designed and experimentally demonstrated. Simulation and measurement results both show a self-healing Airy beam with an efficiency of 23.5% and polarization purity above 20 dB, which approaches the theoretical limitation of the designed Airy beam. Due to the well-performed beam efficiency and polarization purity resulting from the receiving-transmitting metasurface, our design holds great promise for efficient wavefront shaping and facilitates the use of high-purity Airy beams for practical applications.