A low sidelobe transmit beam pattern optimization algorithm based on beam space weighting is proposed. Firstly, the optimization model is established by concerning the beam pattern matching performance while keeping elemental power distribution to be uniform. For the proposed optimization model is nonconvex, semidefinite programming relaxation technique is adopted to transform the nonconvex problem to a convex one. Then, symmetry constraint is constructed for beamspace weighting matrices, which guarantees the rotational invariance property of the received signal. Gaussian randomization technique is utilized to solve the beamspace weighting matrices, therefore, the optimum of original problem can be obtained. Simulation results show that the proposed algorithm can maintain the desired mainlobe shape of the beam pattern as well as decrease the sidelobes, leading to the improvement of Direction Of Arrival(DOA) estimation and target resolution performances.