With the development of multi-variety and small-scale production models, the application of lot streaming technology in manufacturing is becoming increasingly widespread. The lot streaming technology can support continuous overlapping operations to increase productivity. This paper concentrates on studying the hybrid flowshop scheduling problem with consistent sublots (HFSP_CS) with the objective of minimizing the maximum completion time. To solve HFSP-CS, an effective cooperative coevolutionary algorithm (EVCCEA) is proposed by integrating the variable neighborhood descent strategy. In EVCCEA, the HFSP-CS is decomposed, a two-level coding strategy and a novel collaboration mechanism are developed. In addition, two enhanced neighborhood perturbation strategies are proposed to find promising solutions. Finally, the validity of EVCCEA for solving HFSP-CS is proved through extensive experiments.