Most current state-of-the-art text-independent speaker verification systems take probabilistic linear discriminant analysis (PLDA) as their backend classifiers. The model parameters of PLDA is often estimated by maximizing the log-likelihood function. This training procedure focuses on increasing the log-likelihood, while ignoring the distinction between speakers. In order to better distinguish speakers, we propose a multiobjective optimization training for PLDA. Experiment results show that the proposed method has more than 10% relative performance improvement for both EER and the MinDCF on the NIST SRE 2014 i-vector challenge dataset.