Biomass gasification with in-situ CO2 capture, using calcium oxide as sorbent, has attracted increasing interest as a renewable source of high value products through the production of H2 rich syngas, while simultaneously presenting considerable potential for mitigating global warming by reducing CO2 emissions. Many factors influence the final composition of the syngas, such as type and amount of gasifying agent and residence time. Kinetic models play an important role in identifying the specific conditions for controlling the yield and composition of the product gas. When in-situ CO2 capture is used, accurate characterisation of the adsorption reactions in the kinetic scheme is essential for accurate prediction of the H2 rich syngas composition and the overall assessment of the technology. In this work, a kinetic model for biomass gasification with in-situ CO2 capture in a downdraft gasifier is developed. The model is divided into thermochemical stages of pyrolysis, oxidation and reduction in which gasification in a downdraft gasifier occurs, characterised by different compositions and temperature gradients. The model extends the kinetics to the oxidation zone and includes a mechanism for tar oxidation. Given downdraft gasifier designs, a simplification is made where the kinetic behaviour in each of the different stages is modelled separately and in series by a unique set of reactions. The model is validated against two sets of experimental data and different scenarios of equivalence ratio, steam-to-biomass ratio and sorbent-to-biomass ratio are analysed. Sensitivity analysis show that, employing carbon capture, H2 yields can increase of up to 50% under selected conditions. The study aims to provide a better understanding of biomass gasification kinetics and to aid the design and operation of downdraft gasifiers.