New SARS-CoV-2 variants with mutations in the spike glycoprotein have arisen independently at multiple locations and may have functional significance. The combination of mutations in the 501Y.V2 variant first detected in South Africa include the N501Y, K417N, and E484K mutations in the receptor binding domain (RBD) as well as mutations in the N-terminal domain (NTD). Here we address whether the 501Y.V2 variant could escape the neutralizing antibody response elicited by natural infection with earlier variants. We were the first to outgrow two variants of 501Y.V2 from South Africa, designated 501Y.V2.HV001dF and 501Y.V2.HV002. We examined the neutralizing effect of convalescent plasma collected from six adults hospitalized with COVID-19 using a microneutralization assay with live (authentic) virus. Whole genome sequencing of the infecting virus of the plasma donors confirmed the absence of the spike mutations which characterize 501Y.V2. We infected with 501Y.V2.HV001dF and 501Y.V2.HV002 and compared plasma neutralization to first wave virus which contained the D614G mutation but no RBD or NTD mutations. We observed that neutralization of the 501Y.V2 variants was strongly attenuated, with IC50 6 to 200-fold higher relative to first wave virus. The degree of attenuation varied between participants and included a knockout of neutralization activity. This observation indicates that 501Y.V2 may escape the neutralizing antibody response elicited by prior natural infection. It raises a concern of potential reduced protection against re-infection and by vaccines designed to target the spike protein of earlier SARS-CoV-2 variants.