In this paper, we present a covariance regularized probabilistic linear discriminant analysis (CR-PLDA) model for text independent speaker verification. In the conventional simplified PLDA modeling, the covariance matrix used to capture the residual energies is globally shared for all i-vectors. However, we believe that the point estimated i-vectors from longer speech utterances may be more accurate and their corresponding covariances in the PLDA modeling should be smaller. Similar to the inverse 0th order statistics weighted covariance in the i-vector model training, we propose a duration dependent normalized exponential term containing the duration normalizing factor µ and duration extent factor ν to regularize the covariance in the PLDA modeling. Experimental results are reported on the NIST SRE 2010 common condition 5 female part task and the NIST 2014 i-vector machine learning challenge, respectively. For both tasks, the proposed covariance regularized PLDA system outperforms the baseline PLDA system by more than 13% relatively in terms of equal error rate (EER) and norm minDCF values.