Spatially explicit capture-recapture (SECR) models provide an integrative statistical tool for analysing animal movement and population patterns. Although incorporating home range formation with step selection functions into SECR can improve the prediction of animal space use in a heterogeneous landscape, this approach is challenging owing to the sparseness of recapture events.In this study, I developed an advection-diffusion capture-recapture model (ADCR), which is an extension of SECR incorporating home range formation with advection-diffusion formalism, providing a new framework to estimate population density and landscape connectivity. I tested the unbiasedness of the estimator and robustness to the landscape resolution using simulated capture-recapture data generated by a step selection function. I also compared parameter estimates with those from a spatial capture-recapture model based on the least cost path (SCR-LCP) and basic SECR.Population density, connectivity, and home range estimates of ADCR were unbiased over randomly determined sets of true parameters. Although the accuracy of density estimates by ADCR was nearly identical to those of existing models, home range shape could be predicted more accurately by ADCR than by SCR-LCP. ADCR was robust to the choice of landscape resolution, which is a favourable characteristic in random walk-based connectivity measures.ADCR provides unique opportunities to elucidate both individual- and population-level ecological processes from capture-recapture data. By offering a formal link with step selection functions to estimate animal movement, it is suitable for simultaneously modelling with capture-recapture data and animal movement data. This study provides a basis for studies of the interplay between animal movement processes and population patterns.