A robust wideband constant beamwidth beamforming algorithm is proposed to solve the problem of performance degrade of traditional wideband beamforminers when there exists steering vector error. With the spatial response variation (SRV) constrain, a wideband constant beamwidth beamforming algorithm can be obtained by simplifying the response at different frequencies as a reference frequency. Then the robustness of beamformer can be improved by imposing the quadratic constraint for the weight vector. Finally, the optimal weight with a closed form can be solved on the boundary of uncertainty set using the Lagrangian method. Experiments illustrate that the algorithm obtains a desired result to against the look direction estimation error, and achieves a preferable constant beamwidth performance and a high output signal to interference plus noise ratio.