In this paper, low-complexity generalized singular value decomposition (GSVD) based beamforming schemes are proposed for a cognitive radio (CR) network in which multiple secondary users (SUs) with multiple antennas coexist with multiple primary users (PUs). In general, optimal beamforming, which suppresses the interference caused at PUs to below a certain threshold and maximizes the signal-to-interference-plus-noise ratios (SINRs) of multiple SUs simultaneously, requires a complicated iterative optimization process. To overcome the computational complexity, we introduce a signal-to-leakage-plus-noise ratio (SLNR) maximizing beamforming scheme in which the weight can be obtained by using the GSVD algorithm, and does not require any iterations or matrix squaring operations. Here, to satisfy the leakage constraints at PUs, two linear methods, zero forcing (ZF) preprocessing and power allocation, are proposed.