Circular Airy pulsed beams are introduced to significantly optimize the acceleration of neutral Rydberg atoms. Compared with the conventional pulsed Gaussian beams used in the previous report, the circular Airy structure abruptly self-focuses and subsequently propagates with weak diffraction, resulting in a much higher accelerating efficiency for both radial and longitudinal velocities, as well as a longer accelerating range along the propagation axis. The parameter dependencies of the beams on the acceleration are also analyzed.