SARS-CoV-2 variants of concern (VOC) have arisen independently at multiple locations and may reduce the efficacy of current vaccines that target the spike glycoprotein of SARS-CoV-2. Here, using a live-virus neutralization assay, we compared the neutralization of a non-VOC variant with the 501Y.V2 VOC (also known as B.1.351) using plasma collected from adults who were hospitalized with COVID-19 during the two waves of infection in South Africa, the second wave of which was dominated by infections with the 501Y.V2 variant. Sequencing demonstrated that infections of plasma donors from the first wave were with viruses that did not contain the mutations associated with 501Y.V2, except for one infection that contained the E484K substitution in the receptor-binding domain. The 501Y.V2 virus variant was effectively neutralized by plasma from individuals who were infected during the second wave. The first-wave virus variant was effectively neutralized by plasma from first-wave infections. However, the 501Y.V2 variant was poorly cross-neutralized by plasma from individuals with first-wave infections; the efficacy was reduced by 15.1-fold relative to neutralization of 501Y.V2 by plasma from individuals infected in the second wave. By contrast, cross-neutralization of first-wave virus variants using plasma from individuals with second-wave infections was more effective, showing only a 2.3-fold decrease relative to neutralization of first-wave virus variants by plasma from individuals infected in the first wave. Although we tested only one plasma sample from an individual infected with a SARS-CoV-2 variant with only the E484K substitution, this plasma sample potently neutralized both variants. The observed effective neutralization of first-wave virus by plasma from individuals infected with 501Y.V2 provides preliminary evidence that vaccines based on VOC sequences could retain activity against other circulating SARS-CoV-2 lineages.