The multi-way join query plays a fundamental role in many big data analytic scenarios. Recently, the hybrid join query is becoming increasingly important. However, the existing one-round and multi-round algorithms have limitations in the process of the hybrid query. In this paper, we present a novel hybrid structure-aware multi-way join algorithm called HyMJ, which combines the one-round and multi-round algorithms to compute the hybrid query efficiently. First, we propose the query structure graph (QSG) to represent the internal query structure of a given join query and the query structure decomposition tree (QSDT) to represent the structure-aware query plan. Each internal node of the QSDT denotes a subquery with a cyclic or acyclic query structure. Then, we design a graph contraction based algorithm to construct QSDT from QSG. Furthermore, to select the optimal join strategy for each subquery in the QSDT, we introduce a heuristic strategy selection model. Experimental results on Apache Spark reveal that HyMJ outperforms both the one-round and multi-round algorithms for hybrid multi-way join queries on real-world datasets.