Linear discriminant analysis-probabilistic linear discriminant analysis (LDA-PLDA) is a standard and effective backend in the field of speaker verification. The object of LDA is to perform dimensionality reduction while minimizing within-class covariance and maximizing between-class covariance. For a target class (or speaker), our task is to make a binary decision about whether a test utterance is from a specific target speaker. Generally, the nontarget test utterances that are close to the target speaker are easily misjudged. Inspired by this idea, we propose a local pairwise linear discriminant analysis (LPLDA) algorithm. This new method focuses on maximizing the local pairwise covariance, which represents the local structure between the target class samples and neighboring nontarget class samples, instead of the between-class covariance, which represents the global structure of the data. Experiments on the NIST SRE 2010, 2014, and 2016 database show that, the proposed LPLDA-PLDA backend has significant performance improvements over the LDA-PLDA backend.