Ab initio and density functional calculations are conducted to investigate the radicalization processes and radical catalysis of biomass sugars. Structural alterations due to radicalization generally focus on the radicalized sites, and radicalization affects H-bonds in D-fructofuranose more than in D-glucopyranose, potentially with outcome of new H-bonds. Performances of different functionals and basis sets are evaluated for all radicalization processes, and enthalpy changes and Gibbs free energies for these processes are presented with high accuracy, which can be referenced for subsequent experimental and theoretical studies. It shows that radicalization can be utilized for direct transformation of biomass sugars, and for each sugar, C rather than O sites are always preferred for radicalization, thus suggesting the possibility to activate C-H bonds of biomass sugars. Radical catalysis is further combined with Brønsted acids, and it clearly states that functionalization fundamentally regulates the catalytic effects of biomass sugars. In presence of explicit water molecules, functionalization significantly affects the activation barriers and reaction energies of protonation rather than dehydration steps. Tertiary butyl and phenyl groups with large steric hindrances or hydroxyl and amino groups resulting in high stabilities for protonation products drive the protonation steps to occur facilely at ambient conditions.