The recent outbreak of the highly contagious coronavirus disease 2019 (COVID-19) caused by the novel coronavirus SARS-CoV-2 has created a global health crisis with socioeconomic impacts. Although, recently, vaccines have been approved for the prevention of COVID-19, there is still an urgent need for the discovery of more efficacious and safer drugs especially from natural sources. In this study, a number of quinoline and quinazoline alkaloids with antiviral and/or antimalarial activity were virtually screened against three potential targets for the development of drugs against COVID-19. Among seventy-one tested compounds, twenty-three were selected for molecular docking based on their pharmacokinetic and toxicity profiles. The results identified a number of potential inhibitors. Three of them, namely, norquinadoline A, deoxytryptoquivaline, and deoxynortryptoquivaline, showed strong binding to the three targets, SARS-CoV-2 main protease, spike glycoprotein, and human angiotensin-converting enzyme 2. These alkaloids therefore have promise for being further investigated as possible multitarget drugs against COVID-19.