In the present study we explore how annual variation in climate (late wet-season rainfall) affects population demography in a gape-limited obligate piscivorous predator, the Arafura filesnake Acrochordus arafurae in the Australian tropics. These aquatic snakes display extreme sexual dimorphism, with body sizes and relative head sizes of females much larger than those of males. Two consecutive years with low rainfall during the late wet season reduced the abundance of small but not large sized fish. Although snake residual body mass (RBM, calculated from a general linear regression of ln-transformed mass to ln-SVL) decreased after the first year with low prey availability, it was not until the second year that reduced prey abundance caused a dramatic decline in filesnake survival, and hence in population numbers. Thus, our results suggest that most snakes survived the first year of reduced prey abundance, but a successive year with low prey availability proved fatal for many animals. However, the effects of prey scarcity on RBM and survival fell disproportionately on some size classes of snakes. Medium-sized animals (large males and intermediate-sized females) were affected more dramatically than were small or large snakes. We attribute the higher survival of small snakes to their lower energy needs compared to medium-sized individuals, and the higher survival of large snakes to the continued abundance of large prey (mainly large catfish). Two successive years with low abundance of smaller sized prey thus massively modified the size-structure of the filesnake population, virtually eliminating large males and intermediate-sized females. Our field data provide a clear demonstration of the ways in which stochastic variation in climatic conditions can have dramatic effects on predator population demography, mediated via effects on prey availability.