Fish discards and by-products can be transformed into high value-added products such as fish protein hydrolysates (FPH) containing bioactive peptides. Protein hydrolysates were prepared from different parts (whole fish, skin and head) of several discarded species of the North-West Spain fishing fleet using Alcalase. All hydrolysates had moisture and ash contents lower than 10% and 15%, respectively. The fat content of FPH varied between 1.5% and 9.4% and had high protein content (69.8–76.6%). The amino acids profiles of FPH are quite similar and the most abundant amino acids were glutamic and aspartic acids. All FPH exhibited antioxidant activity and those obtained from Atlantic horse mackerel heads presented the highest 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical scavenging activity, reducing power and Cu²⁺ chelating activity. On the other hand, hydrolysates from gurnard heads showed the highest ABTS radical scavenging activity and Fe²⁺ chelating activity. In what concerns the α-amylase inhibitory activity, the IC₅₀ values recorded for FPH ranged between 5.70 and 84.37 mg/mL for blue whiting heads and whole Atlantic horse mackerel, respectively. α-Glucosidase inhibitory activity of FPH was relatively low but all FPH had high Angiotensin Converting Enzyme (ACE) inhibitory activity. Considering the biological activities, these FPH are potential natural additives for functional foods or nutraceuticals.