Justifications are minimal subsets of an ontology that entail a given conclusion. Computing justifications provides a concise explanation of the entailment. Even though computing one justification can be done in polynomial time for tractable Description Logics such as EL+, computing all justifications is hard and often challenging for real-world ontologies. In this paper, we propose a new approach to compute all justifications based on a representation of EL+-ontologies by hyper-graphs. Then, the main idea is to reformulate justifications as special paths called H-paths in the hyper-graph associated with a given ontology. The advantage of this setting is that, most of the time, it reduces the number of the inference rules applied to derive a given conclusion, and this accelerates the enumeration of justifications relying on these inference rules. We validate our approach by running real-world ontology experiments. Our hyper-graph based approach outperforms PULi, the state of the art algorithm. For instance, for the ontology galen7, for which PULi performed the worst, our method generated ten times fewer inference rules on average and accelerated PULi up to three times.