COVID-19 is a contagious multisystem inflammatory disease caused by a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). We studied the efficacy of Aprotinin (nonspecific serine proteases inhibitor) in combination with Avifavir® or Hydroxychloroquine (HCQ) drugs, which are recommended by the Russian Ministry of Health for the treatment therapy of moderate COVID-19 patients. This prospective single-center study included participants with moderate COVID-19-related pneumonia, laboratory-confirmed SARS-CoV-2, and admitted to the hospitals. Patients received combinations of intravenous (IV) Aprotinin (1,000,000 KIU daily, 3 days) and HCQ (cohort 1), inhalation (inh) treatment with Aprotinin (625 KIU four times per day, 5 days) and HCQ (cohort 2) or IV Aprotinin (1,000,000 KIU daily for 5 days) and Avifavir (cohort 3). In cohorts 1–3, the combination therapy showed 100% efficacy in preventing the transfer of patients (n = 30) to the intensive care unit (ICU). The effect of the combination therapy in cohort 3 was the most prominent, and the median time to SARS-CoV-2 elimination was 3.5 days (IQR 3.0–4.0), normalization of the CRP concentration was 3.5 days (IQR 3–5), of the D-dimer concentration was 5 days (IQR 4 to 5); body temperature was 1 day (IQR 1–3), improvement in clinical status or discharge from the hospital was 5 days (IQR 5–5), and improvement in lung lesions of patients on 14 day was 100%.