In order to solve the problem of performance degradation due to the imprecise knowledge of the array steering vector and inaccurate estimation of the sample covariance matrix. A new approach based on beamspace steering vector estimation for robust adaptive beamforming is presented in this paper. Firstly, by using the complementary set of the spatial sector in which the actual steering vector lies, beamspace transformation matrix can be constructed to ensure that the signal of interest is removed from the sampling covariance matrix. Then a method for beamspace steering vector estimation is derived, and mathematically expressed as the nonconvex Quadratically Constrained Quadratic Programs (QCQP) problem with one non-convex quadratic equality constraint, which can be successfully solved by using SemiDefinite Relaxation (SDR) techniques. Simulation results show the effectiveness of the proposed algorithm.