Finite impulse response （FIR） filters are generally used in the design of traditional polynomial broadband beamformers. A generalized polynomial broadband beamformer is proposed by using the orthogonal basis filter instead of FIR filter of the traditional design in this paper. The proposed polynomial broadband beamformer can be regarded as an extension of the traditional polynomial broadband beamformers， so its structure is more flexible. In order to enhance the robustness of the generalized polynomial broadband beamformer， a robust optimization design method based on average performance optimization criterion is further proposed. The poles of the orthogonal basis filter are optimized by particle swarm optimization in this method， so that the performance of the polynomial broadband beamformer can be improved by using the freedom provided by the poles. By introducing the spatial derivative constraint of array response， the orientation deviation of beam mainlobe caused by finite polynomial interpolation is reduced. The simulation results show that， compared with the traditional design method of polynomial structure， the proposed design method can obtain better frequency invariant performance and robustness， effectively improve the orientation accuracy of beam mainlobe， and improve the directivity index of polynomial broadband beamformers.