Probabilistic　linear　discriminant　analysis　(PLDA)　is　a　very　effective　feature　extraction　approach　and　has　obtained　extensive　and　successful　applications　in　supervised　learning　tasks.　It　employs　the　squared　L-2-norm　to　measure　the　model　errors,　which　assumes　a　Gaussian　noise　distribution　implicitly.　However,　the　noise　in　real-life　applications　may　not　follow　a　Gaussian　distribution.　Particularly,　the　squared　L-2-norm　could　extremely　exaggerate　data　outliers.　To　address　this　issue,　this　article　proposes　a　robust　PLDA　model　under　the　assumption　of　a　Laplacian　noise　distribution,　called　L1-PLDA.　The　learning　process　employs　the　approach　by　expressing　the　Laplacian　density　function　as　a　superposition　of　an　infinite　number　of　Gaussian　distributions　via　introducing　a　new　latent　variable　and　then　adopts　the　variational　expectation-maximization　(EM)　algorithm　to　learn　parameters.　The　most　significant　advantage　of　the　new　model　is　that　the　introduced　latent　variable　can　be　used　to　detect　data　outliers.　The　experiments　on　several　public　databases　show　the　superiority　of　the　proposed　L1-PLDA　model　in　terms　of　classification　and　outlier　detection.