In the era of big data, focused analysis for diverse topics with a short response time becomes an urgent demand. As a fundamental task, information filtering therefore becomes a critical necessity. In this paper, we propose a novel deep relevance model for zero-shot document filtering, named DAZER. DAZER estimates the relevance between a document and a category by taking a small set of seed words relevant to the category. With pre-trained word embeddings from a large external corpus, DAZER is devised to extract the relevance signals by modeling the hidden feature interactions in the word embedding space. The relevance signals are extracted through a gated convolutional process. The gate mechanism controls which convolution filters output the relevance signals in a category dependent manner. Experiments on two document collections of two different tasks (i.e., topic categorization and sentiment analysis) demonstrate that DAZER significantly outperforms the existing alternative solutions, including the state-of-the-art deep relevance ranking models.