In this paper, a generalized likelihood ratio test (GLRT) is proposed for cyclostationary multi-antenna spectrum sensing in cognitive radio systems, which takes into account the cyclic autocorrelations obtained from all the receiver antennas and the cyclic cross-correlations obtained from all pairs of receiver antennas. The proposed GLRT employs a different hypotheses problem formulation and a different asymptotic covariance estimation method, which are proved to be more suitable for multi-antenna systems than those employed by the $Dandawat{acute{e}}$-Giannakis algorithm. Moreover, we derive the asymptotic distributions of the proposed test statistics, and prove the constant false alarm rate property of the proposed algorithm. Extensive simulations are conducted, showing that the proposed GLRT can achieve better detection performance than the $Dandawat{acute{e}}$-Giannakis algorithm and its extension for multi-antenna cases.