The x-vector maps segments of arbitrary duration to vectors of fixed dimension using deep neural network. Combined with the probabilistic linear discriminant analysis (PLDA) backend, the x-vector/PLDA has become the dominant framework in text-independent speaker verification. Nevertheless, how to extract the x-vector appropriate for the PLDA backend is a key problem. In this paper, we propose a Gaussian noise constrained network (GNCN) to extract xvector, which adopts a multi-task learning strategy with the primary task classifying the speakers and the auxiliary task just fitting the Gaussian noises. Experiments are carried out using the SITW database. The results demonstrate the effectiveness of our proposed method