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 neutralizing activity. A third SARS-CoV-2 vaccine dose increased median anti-spike (1.6-fold) and receptor-binding domain (1.5-fold) IgG, as well as pseudoneutralization against VOCs (2.5-fold versus Delta). However, IgG and neutralization activity were significantly lower than healthy controls (p<0.001); 32% of SOTRs had zero detectable nAb against Delta after third vaccination. Correlation with nAb was seen at anti-spike IgG >4 AU on the clinical assay and >10^4 AU on the 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.