MIMO system is a technology to realize high data rates and high capacity. Among various MIMO systems, Eigenbeam MIMO (E-MIMO) system achieves the theoretical maximum capacity. The E-MIMO system uses eigenvectors of channel autocorrelation matrix as transmit and receive weights. As a method to find these eigenvectors, eigenvalue decomposition or singular value decomposition (SVD) are generally well-known. In this paper, we propose a least mean square (LMS) based algorithm to find the transmit and receive weights without significant increase of computational complexity for E-MIMO system. Computer simulation shows that the proposed algorithm gives almost the same performance as that of SVD.