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Abstract Background In fish, the most studied production traits in terms of heritability are body weight or growth, stress or disease resistance, while heritability of cortisol levels, widely used as a measure of response to stress, is less studied. In this study, we have estimated heritabilities of two growth traits (body weight and length) and of cortisol response to confinement stress in the European sea bass. Findings The F1 progeny analysed (n = 922) belonged to a small effective breeding population with contributions from an unbalanced family structure of just 10 males and 2 females. Heritability values ranged from 0.54 (±0.21) for body weight to 0.65 (±0.22) for standard body length and were low for cortisol response i.e. 0.08 (±0.06). Genetic correlations were positive (0.94) between standard body length and body weight and negative between cortisol and body weight and between cortisol and standard body length (−0.60 and −0.55, respectively). Conclusion This study confirms that in European sea bass, heritability of growth-related traits is high and that selection on such traits has potential. However, heritability of cortisol response to stress is low in European sea bass and since it is known to vary greatly among species, further studies are necessary to understand the reasons for these differences.