Attention networks, a deep neural network architecture inspired by humans' attention mechanism, have seen significant success in image captioning, machine translation, and many other applications. Recently, they have been further evolved into an advanced approach called multi-head self-attention networks, which can encode a set of input vectors, e.g., word vectors in a sentence, into another set of vectors. Such encoding aims at simultaneously capturing diverse syntactic and semantic features within a set, each of which corresponds to a particular attention head, forming altogether multi-head attention. Meanwhile, the increased model complexity prevents users from easily understanding and manipulating the inner workings of models. To tackle the challenges, we present a visual analytics system called SANVis, which helps users understand the behaviors and the characteristics of multi-head self-attention networks. Using a state-of-the-art self-attention model called Transformer, we demonstrate usage scenarios of SANVis in machine translation tasks. Our system is available at http://short.sanvis.org.