Passive immunization with convalescent plasma (CP) is being evaluated as a treatment for COVID-19. A multicentre, open-label, randomized, controlled trial was conducted in India in which patients received either best standard of care (BSC) (n = 229) or BSC coupled with two 200 ml doses of CP (n = 235). Despite lower viral RNA measured in patients who received CP, there was no difference in 28-day mortality or progression to severe disease between treatment arms. Importantly, 83% of study participants showed detectable neutralizing antibodies (nAbs) at enrolment and nAb titres did not change after treatment. Although this trial failed to demonstrate therapeutic efficacy, future investigations using CP pre-screened for higher nAb titres or treating nAb-naive patients may be warranted.