An adaptive-weight fast-Fourier-transform-based iterative algorithm is proposed for far-field flat-top beam shaping. This algorithm inherits the projection optimization idea from the Gerchberg-Saxton algorithm, but the far-field amplitude for inverse fast Fourier transform is adaptively modified by using a novel optimized adaptive-weight strategy. First, the application of this method to square flat-top intensity-profile beam shaping is discussed as an example. The pure-phase distribution simulated by 100 iterations of this method concentrates 93.89% of the incident laser energy into the desired region and the root mean square error (RMSE) of the tailored flat-top intensity profile is 0.0094. Less than 20 iterations of this method concentrate more than 90% of the incident laser energy into the desired region and the RMSE of the tailored flat-top intensity profile is under 0.05. Then, the applicability of the method to designing the phase distributions for variable-shape or variable-diameter flat-top beam shaping is demonstrated.