Codebook design is a key point in beam-forming which is necessary for millimetre Wave (mmWave) communication to compensate its huge free space path loss. In beam-forming codebook, the transmitter and the receiver cooperate to select the optimum pre-designed code vectors to satisfy robust, efficient, and reliable transmission link between two pairs. In our study, we propose a new codebook structure based on unique phase states. Based on the Array Factor (AF) and Signal-to-Noise Ratio (SNR), the proposed codebook is compared and evaluated with the uniform weighting codebook, circular array codebook, and IEEE 802.15.3c standard codebook. The results show that the proposed codebook achieves comparable SNR and array directivity with the IEEE 802.15.3c, but higher peak and wide dynamic range of SNR and better array directivity compared with the uniform weighting and circular antenna codebooks. Thus, the proposed codebook is expected to improve signal quality and increase user throughput significantly.