This paper presents a novel user selection method based on the signal-to-interference-plus-noise ratio (SINR), which is approximated using limited feedback data at the base stations (BSs) of multiple user multiple-input multiple-output (MU-MIMO) systems. In the proposed system, the codebook vector index, the quantization error obtained from the correlation between the measured channel and the codebook vector, and the measured value of the largest singular value are fed back from each user to the BS. The proposed method not only generates precoding vectors that are orthogonal to the precoding vectors of the previously selected users and are highly correlated with the codebook vector of each user but also adopts the quantization error in approximating the SINR, which eventually provides a significantly more accurate SINR than the conventional SINR-based user selection techniques. Computer simulations show that the proposed method enhances the sum rate of the conventional SINR-based methods by at least 2.4 (2.62) bps/Hz when the number of transmit antennas and number of receive antennas per user terminal is 4 and 1(2), respectively, with 100 candidate users and an SNR of 30 dB.