To date, no specific drug has been discovered for the treatment of COVID-19 and hence, people are in a state of anxiety. Thus, there is an urgent need to search for various possible strategies including nutritional supplementation. In this study, we have tried to provide a reference for protein supplementation. Specifically, 20 marine fish proteins were subjected to in silico hydrolysis by gastrointestinal enzymes, and a large number of active peptides were generated. Then, the binding abilities of these peptides to SARS-CoV-2 main protease and monoamine oxidase A were assessed. The results showed that NADH dehydrogenase could be a good protein source in generating potent binders to the two enzymes, followed by cytochrome b. In addition, some high-affinity oligopeptides (VIQY, ICIY, PISQF, VISAW, AIPAW, and PVSQF) were identified as dual binders to the two enzymes. In summary, the supplementation of some fish proteins can be helpful for COVID-19 patients; the identified oligopeptides can be used as the lead compounds to design potential inhibitors against COVID-19 and anxiety.