Sustained swimming induces beneficial effects on growth and energy metabolism in some fish species. However, the absence of a standardized exercise regimen that guarantees an optimal response to physical activity is due to the anatomical, behavioral, and physiological differences among species, and the different conditions of tests applied, which are especially notable for the early stages of cultured species. The objective of this study was to assess the growth and metabolic responses of European sea bass submitted to continuous and moderate exercise exposure, selecting a practical swimming speed from swimming tests of groups of five fingerlings. The exercise-effects trial was carried out with 600 sea bass fingerlings (3–5 g body weight) distributed in two groups (control: voluntary swimming; exercised: under sustained swimming at 1.5 body lengths·s−1). After 6 weeks, growth parameters and proximal composition of both muscles were not altered by sustained swimming, but an increased synthetic capacity (increased RNA/DNA ratio) and more efficient use of proteins (decreased ΔN15) were observed in white muscle. The gene expression of mitochondrial proteins in white and red muscle was not affected by exercise, except for ucp3, which increased. The increase of UCP3 and Cox4 protein expression, as well as the higher COX/CS ratio of enzyme activity in white muscle, pointed out an enhanced oxidative capacity in this tissue during sustained swimming. In the protein expression of red muscle, only CS increased. All these metabolic adaptations to sustained exercise were also reflected in an enhanced maximum metabolic rate (MMR) with higher aerobic scope (AMS) of exercised fish in comparison to the non-trained fish, during a swimming test. These results demonstrated that moderate sustained swimming applied to sea bass fingerlings can improve the physical fitness of individuals through the enhancement of their aerobic capacities.