Knowledge graph (KG) embedding techniques represent entities and relations as low-dimensional and continuous vectors. This enables KG machine learning models to be easily adapted for KG reasoning, completion, and querying tasks. However, learned dense vectors are inefficient for large-scale similarity computations. Learning-to-hash is to a method that learns compact binary codes from high-dimensional input data and provides a promising way to accelerate efficiency by measuring the Hamming distance instead of Euclidean distance. Alternatively, a dot-product is used in a continuous vector space. Unfortunately, most learning-to-hash methods cannot be directly applied to KG structure encoding because they focus on similarity preservation between images. In this paper, we introduce a novel end-to-end learning-to-hash framework for encoding incomplete KGs and graph queries in a Hamming space. To preserve KG structure information, from embeddings to hash codes, and address the ill-posed gradient issue in the optimization, we utilize a continuation method (with convergence guarantees) to jointly encode queries and KG entities using geometric operations. The hashed embedding of a query can be utilized to discover target entities from incomplete KGs whilst the efficiency has been greatly improved. To evaluate the proposed framework, we have compared our model to state-of-the-art methods commonly used in real-world KGs. Extensive experimental results show that our framework not only significantly speeds up the search process, but also provides good results when unanswerable queries are caused by incomplete information.1