Response delays to predator attack may be adaptive, suggesting that latency to respond does not always reflect predator detection time, but can be a decision based on starvation–predation risk trade-offs. In birds, some anti-predator behaviours have been shown to be correlated with personality traits such as activity level and exploration. Here, we tested for a correlation between exploration behaviour and response latency time to a simulated fish predator attack in a fish species, juvenile convict cichlids (Amatitlania nigrofasciata). Individual focal fish were subjected to a standardized attack by a robotic fish predator while foraging, and separately given two repeated trials of exploration of a novel environment. We found a strong positive correlation between exploration and time taken to respond to the predator model. Fish that were fast to explore the novel environment were slower to respond to the predator. Our study therefore provides some of the first experimental evidence for a link between exploration behaviour and predator-escape behaviour. We suggest that different behavioural types may differ in how they partition their attention between foraging and anti-predator vigilance.