Ontology-mediated data access and management systems are rapidly emerging. Besides standard query answering, there is also a need for such systems to be coupled with explanation facilities, in particular to explain missing query answers (i.e. desired answers of a query which are not derivable from the given ontology and data). This support is highly demanded for debugging and maintenance of big data, and both theoretical results and algorithms proposed. However, existing query explanation algorithms either cannot scale over relative large data sets or are not guaranteed to compute all desired explanations. To the best of our knowledge, no existing algorithm can efficiently and completely explain conjunctive queries (CQs) w.r.t. ELH1 ontologies. In this paper, we present a hybrid approach to achieve this. An implementation of the proposed query explanation algorithm has been developed using an off-the-shelf Prolog engine and a datalog engine. Finally, the system is evaluated over practical ontologies. Experimental results show that our system scales over large data sets.