Capturing and sequestering carbon dioxide (CO2) can provide a route to partial mitigation of climate change associated with anthropogenic CO2 emissions. Here we report a comprehensive theoretical study of CO2 adsorption on two phases of boron, α-B12 and γ-B28. The theoretical results demonstrate that the electron deficient boron materials, such as α-B12 and γ-B 28, can bond strongly with CO2 due to Lewis acid-base interactions because the electron density is higher on their surfaces. In order to evaluate the capacity of these boron materials for CO2 capture, we also performed calculations with various degrees of CO2 coverage. The computational results indicate CO2 capture on the boron phases is a kinetically and thermodynamically feasible process, and therefore from this perspective these boron materials are predicted to be good candidates for CO2 capture.