The objective of the Quay Crane Scheduling Problem (QCSP) is to determine the schedule that minimizes the makespan (completion time of the last task) given a set of tasks (loading or unloading operations to/from a container vessel), the precedence and non-simultaneity relations between them and a set of quay cranes. A heuristic solution method to explore unidirectional schedules (where the quay cranes do not change their moving sense after the initial positioning and have identical sense of movement) has been previously proposed in the literature. Although the heuristic is able to find optimal unidirectional schedules for small instances, its performance decreases when the size grows. In this work, a Variable Neighbourhood Search (VNS) for the QCSP which incorporates a memory structure to keep high quality solutions (elite solutions) is proposed. Elite solutions are then combined to construct initial solutions for the VNS. The computational experiments confirm that the VNS significantly outperforms the results obtained by the previous work from the literature.