A robust beamformer design is proposed for a spectrum sharing CR network consisting of multiple secondary users (SUs) in the presence of multiple primary users (PUs). The proposed algorithm aims to maximize the worst case signal-to-interference-plus-noise ratio (SINR) of the SUs while limiting the interference leakage to PUs. Since it may be difficult to obtain perfect information about the channels between the SU basestation and the PUs, we consider errors in the PU channel estimates and design beamformers to limit interference leakage to PU below a specific threshold with a certain probability. The simulation results demonstrate that the proposed beamformer design has the ability to maximize the worst case SINR (balanced SINR) while controlling the interference leakage to PUs.