This paper presents a dataset obtained from fifty-two laboratory experiments of nappe oscillations on free overfall structures. Data were collected on two complementary experimental setups, each consisting of a linear weir model. The dataset covers test configurations involving varied geometric parameters (i.e. weir crest shape, weir width, fall height and nappe confinement) and inflow discharges. The following experimental data were produced: assessment of nappe oscillation occurrence and associated frequencies. The later measurements were performed using characterization techniques (image and sound analysis) developed for this research. Reuse of the collected data will support efforts to improve the understanding of the physical processes underpinning nappe oscillation and to validate numerical modelling of the phenomenon.