Coverage optimization is an important task, which directly affects the performance of cellular networks. It is difficult to correct the weak coverage and the over coverage simultaneously using existing methods such as adjusting antenna downtilts and/or transmit powers of sectors. In this paper, a novel coverage optimization method based on multi-sector joint beamforming is proposed, so that weak coverage area and over coverage area can be decreased simultaneously. A heuristic algorithm based on the semidefinite relaxation is then developed to obtain antenna array excitation weights with low computational complexity. Simulation results show that the performance of our algorithm is superior to that of antenna downtilt optimization algorithm.