Abstract: This paper proposes a beampattern optimization method for superdirective frequency-invariant beamforming with circular sensor arrays. Firstly, the previously proposed beampattern-synthesis-based superdirective beamforming method is briefly reviewed. Since the weighting vectors at different frequencies are all expressed as analytical functions of the desired weighting vector based on the criterion of minimizing the mean square error between the desired and synthesized beampatterns, the directivity factor, the sensitivity function, and the minimum mean square error can be all formulated as functions of the desired weighting vector. Then, a multi-constraint optimization problem is proposed, which can obtain the optimal desired beampattern subject to directivity, robustness, and frequency-invariance constraints. The superdirective frequency-invariant beampatterns at other frequencies can be directly synthesized using the previously derived analytical functions. The good performance of the proposed method is demonstrated using simulations and experimental data.