The paper proposes a codebook design to support beamforming mechanism in a wide band millimeter-wave 60GHz wireless personal area networks (60GHz WPANs) in a realistic millimeter-wave environment. The codebooks are designed symmetrically in order to mitigate the possible beam shift due to the large differences of wave lengthes at different sub-bands of a wide band communication system. In order to provide a high data rate and high performance with minimum power consumption in 60GHz systems, the codebooks are generated with 90 degree phase resolution without amplitude adjustment. The codebooks are designed for different numbers of antenna elements, supporting a multitude of antenna configurations. The paper provides codebook design mechanism, some example codebooks and some analysis on antenna gain loss due to phase shift errors of phase shifters. Simulation results shows that: (1) To keep the gain loss at the intersections of any two patterns inside the codebook lower than 1dB, the number of patterns inside the codebook shall be at least 2 times of the number of antenna elements used for pattern generation; (2) The designed codebooks are robust to phase shift errors: the gain loss is lower than 1dB with only 10% outage probability when standard deviation of phase shift errors at phase shifters is 0.5 [28.6 degree]. The proposed codebooks are a feasible design, they are the key basis of the beamforming protocol in 60GHz WPANs (IEEE 802.15.3c).