Anxiety and depression are two conditions whose incidence increased in the context of COVID-19. Administration of current therapies based on anxiolytic and antidepressant drugs can result in adverse reactions and even potential dangers in the case of some patients like older adults and elderly patients. Aiming to identify safer treatments, we used molecular docking to screen twenty natural compounds against γ-aminobutyric acid A receptor (GABAA receptor), a major drug target in anxiety, and against serotonin transporter (SERT), a major drug target in depression. The list of compounds included molecules that were previously reported as beneficial in the two conditions. In the case of all molecules, we predicted their drug-likeness, bioavailability and pharmacokinetic profiles. Molecular docking has showed that the top five molecules in terms of affinity for GABAA receptor are luteolin, baicalein, myricetin, chrysin and curcumin. In the case of SERT, the top five ligands resulted to be myricetin, luteolin, curcumin, apigenin and fisetin. According to the predictions performed here, these molecules comply with drug-likeness rules, are bioavailable and non-toxic, present a high intestinal absorption and are distributed to the central nervous system. Our results point toward luteolin, myricetin and curcumin as common ligands for GABAA receptor and SERT, suggesting their beneficial effect in both anxiety and depression.