Probabilistic Linear Discriminant Analysis (PLDA) is a popular tool in open-set classification/verification tasks. However, the Gaussian assumption underlying PLDA prevents it from being applied to situations where the data is clearly non-Gaussian. In this paper, we present a novel nonlinear version of PLDA named as Neural Discriminant Analysis (NDA). This model employs an invertible deep neural network to transform a complex distribution to a simple Gaussian, so that the linear Gaussian model can be readily established in the transformed space. We tested this NDA model on a speaker recognition task where the deep speaker vectors (x-vectors) are presumably non-Gaussian. Experimental results on two datasets demonstrate that NDA consistently outperforms PLDA, by handling the non-Gaussian distributions of the x-vectors.