This paper investigates the coordinated beam-forming design for multi-cell MISO downlink beamforming system, aiming at maximizing the sum rate. In the proposed scheme, convex approximation approach is used to first recast the primal non-convex problem into an approximate problem of minimizing the sum of weighted inverse SINR. Then, an alternating optimization method is developed to address the approximate problem based on uplink-downlink duality. We show that our solution is globally optimal in the case of two-BS cooperation with a total power constraint, and is also effective in a general case. When extending to per-BS power constraints, an alternating optimization algorithm with provable convergence to stationary point is proposed following a similar procedure. Our simulation results show that the proposed scheme has a fast convergence and achieves a sum rate performance very close to the optimal performance obtained by exhaustive search.