This paper focuses on a downlink beamforming problem in the cognitive radio (CR) communication system where primary users (PU) coexist with secondary users (SU). It is assumed that the SU transmitter has multiple antennas and transmits data to another SU's single-antenna receiver using the beamforming technique. By properly designing a beamforming vector, SU can maximize its channel gain while maintaining an interference with PU below a predefined level. In order to construct an optimal beamforming vector, the SU transmitter requires knowledge of the downlink channel information of both PU and SU receivers sent on the feedback channel. However, it is impractical to assume that the transmitter has the perfect channel state information (CSI) considering the tremendous feedback overhead. One way to tackle this feedback overhead problem is to use a finite number of feedback bits indicating the index of a predefined codeword in the codebook. We analyze interference to the PU receiver and propose an algorithm to design a beamforming vector considering an error attributed to the partial CSI. The simulation shows that the analysis is quite accurate and that the beamforming vector, designed according to the proposed algorithm, keeps interference to PU below a predefined level while taking into account the error owing to the partial CSI. By using the proposed scheme, the CR system can become more robust against errors attributed to the partial CSI.