Due to the growing demand of data rate and reliability in multi-user wireless applications, multiple-user multiple-input multiple-output (MU-MIMO) precoding schemes are developed to avoid the growing interferences among users. The leakage-based precoding algorithm is a key processing technique that can achieve a higher signal-to-interference noise ratio (SINR) in the MU-MIMO system. The leakage-based precoding scheme requires the generalized eigenvalue decomposition (GEVD) processing to obtain the optimal MIMO precoding matrix for each user based on various constraints. Therefore, this paper presents a GEVD processor for the leakage-based multi-user MIMO precoding. A triangular matrix inversion with block-wise multiplications (TMI-BM) algorithm was proposed to avoid the massive matrix inversions in the original GEVD. The GEVD processor was designed and implemented using a 40μm CMOS technology. The proposed GEVD processor achieves 0.46 Matrices/sec.