Background: COVID-19 convalescent plasma (CCP) is an important antiviral option for selected patients with COVID-19. Materials and Methods: In this open-label, phase 2, clinical trial conducted from 30 April 2020 till 10 May 2021 in the Republic of North Macedonia, we evaluated the efficacy and safety of CCP in hospitalized patients. Treatment was with a single unit of CCP having an anti-RBD IgG concentration higher than 5 AU/mL. Results: There were 189 patients that completed the study, of which 65 (34.4%) had WHO 8-point clinical progression scale score of 3 (requiring hospital care but not oxygen support), 65 (34.4%) had a score of 4 (hospitalized and requiring supplemental oxygen by mask or nasal prongs), and 59 (31.2%) had a score of 5 (hospitalized and requiring supplemental oxygen by non-invasive ventilation or high-flow oxygen). Mean age was 57 years (range 22–94), 78.5% were males, 80.4% had elevated body mass index, and 70.9% had comorbidity. Following CCP transfusion, we observed clinical improvement with increase rates in oxygenation-free days of 32.3% and 58.5% at 24 h and seven days after CCP transfusion, a decline in WHO scores, and reduced progression to severe disease (only one patient was admitted to ICU after CCP transfusion). Mortality in the entire cohort was 11.6% (22/189). We recorded 0% mortality in WHO score 3 (0/65) and in patients that received CCP transfusion in the first seven days of disease, 4.6% mortality in WHO score 4 (3/65), and 30.5% mortality in WHO score 5 (18/59). Mortality correlated with WHO score (Chi-square 19.3, p < 0.001) and with stay in the ICU (Chi-square 55.526, p ≤ 0.001). No severe adverse events were reported. Conclusions: This study showed that early administration of CCP to patients with moderate disease was a safe and potentially effective treatment for hospitalized COVID-19 patients. The trial was registered at clinicaltrials.gov (NCT04397523).