The debate surrounding the role of genetic and environmental factors in shaping behaviour has a long tradition. However, their effects on complex behaviours such as unpredictability in anti-predator strategies remain poorly understood. Behaving unpredictably when escaping predators may increase the prey's chances of survival, especially when prey can rely on a complex habitat providing camouflage and shelter opportunities. We explored the effects of genetic and environmental influences on escape strategies of the steppe grasshopper Chorthippus dorsatus. Individuals from controlled breeding had been randomly assigned to one of two environmental complexity treatments during ontogeny. We then quantified escape behaviour in a large cohort through burst experiments. Using a multivariate double hierarchical animal model, we analysed the effects of pedigree and environmental complexity on both inter- and intra-individual variance in three components of escape behaviour: flight initiation distance (FID), jump distance, and jump angle. Habitat complexity affected average jump angle, but not the average FID or jump distance, nor unpredictability in any of the three traits. Pedigree relatedness accounted for 5%-6% of the total variance in average FID and average jump distance and 7% of the variance in unpredictability in jump angle. Genetic correlations suggest a behavioural syndrome structure in escape strategies that involve FID (a potential indicator of boldness). Our study demonstrates that unpredictability in escape behaviour has the potential to evolve by natural selection, as some of its components are heritable. Furthermore, we show that although habitat complexity represents a strong environmental treatment, its lasting effects during ontogeny on escape behaviour are minimal.