Aquaculture of carnivorous species has strongly relied on fish meal and fish oil for feed formulation; however, greater replacement by terrestrial plant-based products is occurring now. This rapid change in dietary environment has been a major revolution and has to be taken into consideration in breeding programs. The present study analyzes potential consequences of this nutritional tendency for selective breeding by estimating genetic parameters of BW and growth rates estimated by the thermal growth coefficient (TGC) over different periods with extremely different diets. European sea bass (Dicentrarchus labrax L.) from a factorial cross (1,526 fish) between 25 sires and 9 dams were used to estimate heritabilities and genotype by diet interaction. Starting 87 d after fertilization (2.5 g), one-half of the sea bass were fed a diet containing marine products (M), and the other one-half were fed a totally plant-based (PB) diet (without any fish meal or fish oil). The fish were individually tagged, reared in a recirculated system, and genotyped at 13 microsatellites to rebuild parentage of individuals. Body weight and TGC were measured for 335 d until fish fed the M diet reached 108.3 g of BW. These traits were significantly less in fish fed the PB diet (P < 0.05) in the very first stages after the dietary shift, but the difference in TGC between diets rapidly disappeared (P > 0.1). Survival was significantly less in fish fed the PB diet (PB = 64.7%, M = 93.7% after 418 d, P < 0.05). This work identified moderate heritabilities (0.18 to 0.46) for BW with both diets and high genetic correlations between diets (0.78 to 0.93), meaning low genotype by diet interactions, although diets were extremely different. Heritabilities of TGC (0.11 to 0.3) were less than for BW as well as genetic correlations between diets (0.43 to 0.64). Using such extremely different diets, predicted BW gains in different scenarios indicated that selecting fish for growth on a marine diet should be the most efficient way to increase growth on plant-based diets, meaning that, in this case, indirect selection should be more efficient than direct selection.