In this paper, we present a MapReduce-based framework for evaluating SPARQL queries on GPU (named MapSQ) to large-scale RDF datesets efficiently by applying both high performance. Firstly, we develop a MapReduce-based Join algorithm to handle SPARQL queries in a parallel way. Secondly, we present a coprocessing strategy to manage the process of evaluating queries where CPU is used to assigns subqueries and GPU is used to compute the join of subqueries. Finally, we implement our proposed framework and evaluate our proposal by comparing with two popular and latest SPARQL query engines gStore and gStoreD on the LUBM benchmark. The experiments demonstrate that our proposal MapSQ is highly efficient and effective (up to 50% speedup).