We develop PALM-CO₂, a high-resolution urban carbon dioxide transport model with anthropogenic and biogenic carbon emissions. The model is based on an open-source urban flow large eddy simulation (LES) model, PALM, where we implemented a biogenic carbon emission module (Vegetation Photosynthesis and Respiration Model, VPRM) and customised output modules for carbon fluxes. PALM-CO₂ is validated through a case study in London, comprising an 8 by 8 km² domain covering the borough of Camden at a resolution of 10 m. Simulations are driven by reanalysis meteorological forcing and background CO₂ concentrations, while the hourly anthropogenic emissions at 10-m resolution are explicitly derived in this study. Validation against eddy-covariance flux measurements inside the study region confirms that the model captures the diurnal variation of the turbulent transport and anthropogenic emissions. Additional validation against monthly biogenic flux diurnal profiles at a deciduous forest site in Czech Republic further confirms the biogenic flux module. The simulations reveal strong spatial heterogeneity in near-surface CO₂ concentrations driven by building-induced turbulence, diurnal boundary layer evolution, and emission patterns. PALM-CO₂ provides a high-resolution framework for investigating CO₂ transport processes in complex urban and vegetated environments, providing improved quantification of urban emission sources.