We propose and theoretically demonstrate a novel optical fiber with an annular arrayed-waveguide to implement Airy phase and amplitude modulation, and generate an abruptly autofocusing circular Airy beam. The properties of wave propagation in Airy fiber and free space are studied by using the coupled-mode theory and angular spectrum method. The calculated results show that the output beam from such a fiber has a circular Airy-like pattern and can autofocus with the intensity maxima following a parabolic trajectory. We also show that the position of the focus point of the output beam from the Airy fiber can be easily controlled by changing input wavelength.