Oxocarboxylic acids, one of the most important organic species, are detected in aerosols in various environments. Recent studies suggest that the gas-phase reactions between carboxylic acids and SO3 could form carboxylic sulfuric anhydrides, which might participate in nucleation. Here, glyoxylic acid (GA), the most abundant oxocarboxylic acid in the atmosphere, has been selected as an example to study the reactions between oxocarboxylic acids and SO3 and the nucleation potentials of products. The reaction between GA and SO3 that generates glyoxylic sulfuric anhydride (GSA) and the hydrolysis of GSA are investigated using computational methods. The results show that the reaction is almost barrierless, and GSA is stable against water. Additionally, the clusters of GSA and common nucleation species (sulfuric acid and ammonia) are more stable than the analogous clusters of GA, because they have more hydrogen bonds and proton transfers. It suggests that GA tends to transfer itself to a much better nucleation precursor, GSA, through a reaction with SO3, and GSA can drive nucleation and contribute to new particle formation (NPF). This mechanism might be general for all oxocarboxylic acids and could help to deeply understand the roles of oxocarboxylic acids in NPF.