Recently deep learning has been successfully applied to unsupervised active learning. However, current method attempts to learn a nonlinear transformation via an auto-encoder while ignoring the sample relation, leaving huge room to design more effective representation learning mechanisms for unsupervised active learning. In this paper, we propose a novel deep unsupervised Active Learning model via Learnable Graphs, named ALLG. ALLG benefits from learning optimal graph structures to acquire better sample representation and select representative samples. To make the learnt graph structure more stable and effective, we take into account $k$-nearest neighbor graph as a priori, and learn a relation propagation graph structure. We also incorporate shortcut connections among different layers, which can alleviate the well-known over-smoothing problem to some extent. To the best of our knowledge, this is the first attempt to leverage graph structure learning for unsupervised active learning. Extensive experiments performed on six datasets demonstrate the efficacy of our method.