Coordinated Beamforming (CB) is an effective technique to maximize weighted sum rate (WSR) targeting at on-demand network capacity. However, the channel state information (CSI) of the base stations (BSs) far away can’t be measured accurately, which will lead to the invalidation of the traditional WSR-maximization beamformer design and eventually result in capacity decrease. This letter proposes a tractable user-centric CSI model and a robust CB design to maximize WSR with partially accurate CSI. Specifically, the CSI model of the coordinated BSs is built for each user, where the inaccurate CSI of BSs far away from this user is modeled according to its static statistic characteristic. To derive a robust beamformer, deterministic equivalent method is adopted to obtain an approximate closed-form expression of the ergodic sum rate. Moreover, the performance of the robust CB design with different model parameters is considered to provide guidance for practical network deployment. Simulation results show that the proposed robust CB design has 30% capacity gain through careful interference management compared with traditional beamforming.