The ability to provide high data rate is a key measure in 3GPP Long Term Evolution (LTE). Multiple Input Multiple Output (MIMO) has emerged as an technique that increases the data rates in 3G systems. In this paper we study MIMO-OFDM system based on adaptive modulation and investigate the precoding technology. We present a method for adaptive modulation based on eigenvalues and a precoding matrix will be used at the transmitter according to singular value decomposition. A low complexity ratio-based algorithm with good performance is proposed to decide which modulation scheme to be used. The achieved results show that the proposed scheme outperforms basic beamforming with adaptive modulation.