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In this letter, we present a linear precoder design scheme for a cognitive (CR) multi-input multi-output (MIMO) system, where a secondary broadcast channel uses the same spectrum with multiple primary users (PUs). Considering both cooperative feedback from the PUs and local feedback from the secondary users (SUs) to the secondary transmitter (ST), the ST can obtain the quantized information regarding the direction of the channels. The proposed scheme is based on the minimum mean square error (MMSE) criteria and is robust to the channel uncertainties caused by quantization error. The derivation is given under two different levels of interference constraints respectively. Simulation results show the effectiveness of the proposed precoder design scheme.