Vaccine-induced SARS-CoV-2 antibody responses are attenuated in solid organ transplant recipients (SOTRs) and breakthrough infections are more common. Additional SARS-CoV-2 vaccine doses increase anti-spike IgG in some SOTRs, but it is uncertain whether neutralization of variants of concern (VOCs) is enhanced. We tested 47 SOTRs for clinical and research anti-spike IgG, pseudoneutralization (ACE2 blocking), and live-virus neutralization (nAb) against VOCs before and after a third SARS-CoV-2 vaccine dose (70% mRNA, 30% Ad26.COV2.S) with comparison to 15 healthy controls after two mRNA vaccine doses. We used correlation analysis to compare anti-spike IgG assays and focused on thresholds associated with neutralization. A third SARS-CoV-2 vaccine dose increased median total anti-spike (1.6-fold), pseudoneutralization against VOCs (2.5-fold vs. Delta), and neutralizing antibodies (1.4-fold against Delta). However, neutralization activity was significantly lower than healthy controls (p < .001); 32% of SOTRs had zero detectable nAb against Delta after third vaccination compared to 100% for controls. Correlation with nAb was seen at anti-spike IgG >4 Log10 (AU/ml) on the Euroimmun ELISA and >4 Log10 (AU/ml) on the MSD research assay. These findings highlight benefits of a third vaccine dose for some SOTRs and the need for alternative strategies to improve protection in a significant subset of this population.