In this paper, a nonlinear, bounded, distributed secondary control (DSC) method is proposed to coordinate all the distributed generators (DGs) in islanded AC microgrids (MGs). This proposed consensus-based DSC strategy can not only guarantee the restoration control of frequency and voltage but also realize an accurate active power sharing control. Through introducing a nonlinear dynamic from beta cumulative distribution function (CDF), the convergence speed of DSC is accelerated, the asymptotical convergence of DSC is ensured, and the transient overshoot of DSC is diminished compared with traditional DSC. Moreover, by ensuring the Lipchitz continuity characteristic of the control algorithm, the common chattering phenomenon in non-Lipchitz DSC scheme is eliminated. The stability and performance of the proposed DSC are also analyzed in this paper. An islanded AC microgrid test system with four inverter-based DGs is built in MATLAB/SIMULINK to further validate the effeteness of the proposed DSC strategy.