A broadband beamforming algorithm in time-domain with minimum sidelobe and constant beamwidth on convex optimization is proposed.The array response is expressed as a linear function of a set of the finite impulse response(FIR)filter weights.The filter weights are designed in the optimized constraint beamwidth and minimum sidelobes minimizing the sidelobes while guaranteeing the beamwidth invariance.Norm constraint on tap weights and nulls widening constraint in the direction of the interference are also imposed to improve the robustness of the beamformer.The construction process of the desired response and the approaching process of the actual response are combined together to get the global optimal solution.Computationally efficient convex formulation for beamformer design problem is derived.Simulation results demonstrate the satisfactory performance of the proposed algorithm.