The no-wait flow shop scheduling problem (NWFSP) has been achieved a wide variety of researches by scholars as a typical NP-hard problem. In this paper, a construction block inspired variable neighborhood search heuristic algorithm (BBA-VNS) is proposed for solving NWFSP with the goal of maximum completion time. The core idea of BBA is to seek out the best match until all jobs are arranged in the process set. In the BBA, waiting time matrix and matching matrix between two jobs are constructed to obtain an approximate optimal scheduling sequence. In addition, the variable neighborhood search mechanism (VNS) is used to further improve the solution quality which based on block neighborhood structure and insert neighborhood structure. The results on a large-scale benchmark indicate that BBA-VNS is better than the most advanced heuristic algorithm.