Abstract: In order to solve the problem of the output performance degradation of the traditional beamformer caused by traditional adaptive beamforming method in the presence of array error, a robust adaptive wideband constant beamwidth digital beamforming method based on second-order cone programming is proposed. Firstly, a beamformer with constant beamwidth is designed based on the constraint of spatial response variation. Secondly, the minimum output power under the constraint of amplitude inequality is optimized according to the 2-norm error between the array actual steering vector and the ideal steering vector. Finally, the optimization model is solved by second-order cone programming through the redefinition of variables. Numerical simulation results show that the proposed method can solve the robustness problem of wideband digital beamforming to against array error, and can obtain higher array output signal to interference plus noise ratio with lower computational complexity.