This study introduces a novel Curriculum Learning based Probabilistic Linear Discriminant Analysis (CL-PLDA) algorithm for improving speaker recognition in noisy conditions. CL-PLDA operates by initializing the training EM algorithm with cleaner data ( easy examples), and successively adds noisier data ( difficult examples) as the training progresses. This curriculum learning based approach guides the parameters of CL-PLDA to better local minima compared to regular PLDA. We test CL-PLDA on speaker verification task of the severely noisy and degraded DARPA RATS data, and show it to significantly outperform regular PLDA across test-sets of varying duration.