This paper aims at presenting our algorithm used to make submission for the 2013-2014 NIST speaker recognition i-vector challenge. The fixed dimensional i-vector representation of speech utterances provides an opportunity to apply techniques from machine learning community to improve speaker recognition performance. The unlabeled i-vectors provided for development purpose makes the problem more challenging. The proposed method uses the idea of one of the popular robust beamforming techniques named Lineally Constrained Minimum Variance (LCMV), which has been presented in the context of beamforming for signal enhancement. We will show that LCMV can improve performance by building a model from different i-vectors of a given speaker so as to cancel inter-session variability and increase inter-speaker variability. Covariance matrix modification and score normalization using a selection of imposter speakers have been used to further improve performance. As measured by minimum decision cost function defined in the challenge, our result is about 27% better relative to the baseline system.