Abstract: The mainbeam is difficult to maintain in adaptive beamforming for conformal array, and even worse, the sidelobe is very high. To alleviate these problems, an adaptive beamforming method is proposed based on the response vector optimization. Through adaptively adjusting the response vector under the well-maintained mainbeam constraint, the optimal response vector is derived, thus the sub-optimal adaptive weight is obtained. The proposed method converts the non-convex quadratically constrained quadratic optimizing problem into a higher-dimension subspace, then the problem is transformed into a convex optimization problem via SemiDefinite Relaxation (SDR), and then its sub-optimal solution is efficiently achieved. The method not only maintains the desired response of the mainbeam, but also overcomes the disadvantages of high sidelobe resulting from the conventional Linearly Constrained Minimum Variance (LCMV) adaptive approach. Moreover, it is robust against the geometry of the array. Simulation results demonstrate the effectiveness of the proposed method.