Jellyfish blooms occur in marine environments around the world and have been linked to over-fishing, eutrophication and climatic change. In some coastal areas of Norway, the circumglobal Periphylla periphylla has increased to exceptionally high abundances and has replaced fish as the main planktivorous predator despite the ineffectiveness of its non-visual predation compared to visual fish predation. Using data from a bottom-mounted acoustic platform, we collected 12341 in situ measurements of individual vertical movements of large individuals of P. periphylla. These jellyfish are characterized by a stepwise vertical movement. The distribution of their vertical swimming distances was extremely left skewed; about 85% of the swimming distances were less than 3 m, and a few displacements were extremely long with a maximum of 85 m. Chi-square tests of goodness of fit to the tail and Akaike’s information criterion gave overwhelming evidence of the truncated power law. There was a clear diel pattern in the exponent with values significantly larger than 3 during the daytime and significantly lower than 3 at night. This pattern means that P. periphylla switches from relatively limited movements during the day to Lévy-like flights during the night. Since the abundance of zooplankton is large in the P. periphylla fjord, Brownian motion, rather than Lévy flight, is predicted by the optimal foraging hypothesis. It is therefore possible that the Lévy-like search pattern has evolved in the food-scarce oceanic environment, which is the main natural habitat of P. periphylla. Alternatively, the large individuals of the population addressed here may forage on scarcer prey sources than the main prevailing zooplankton in Lurefjorden.