State-of-the-art speaker verification models are based on deep learning techniques, which heavily depend on the handdesigned neural architectures from experts or engineers. We borrow the idea of neural architecture search(NAS) for the textindependent speaker verification task. As NAS can learn deep network structures automatically, we introduce the NAS conception into the well-known x-vector network. Furthermore, this paper proposes an evolutionary algorithm enhanced neural architecture search method called Auto-Vector to automatically discover promising networks for the speaker verification task. The experimental results demonstrate our NAS-based model outperforms state-of-the-art speaker verification models.