Magneto-optical imaging of dendritic flux instability is reported for NbN films exposed to magnetic fields ramped at a fast rate (0.1-3.2 kT s −1). The results show that as the magnetic ramp rate increases, the temperature and field range of the instability extends significantly. In particular, the lower and upper threshold fields (H th 1 and H , th 2 respectively) that bound the field range for dendritic instability are affected. The upper field is found to increase linearly with the applied field sweep rate, a behavior which is discussed in terms of a recent theoretical work (Vestgarden et al 2016 Phys. Rev. B 73 174511). The extended instability range should be taken into account in applications in which the superconducting films are exposed to rapid changes in the magnetic field.