Pollutant transport due to the turbulent wind flow around buildings is a complex phenomenon which is challenging to reproduce with Computational Fluid Dynamics (CFD). In the present study we use Large-Eddy Simulation (LES) to investigate the turbulent mass transport mechanism in the case of gas dispersion around an isolated cubical building. Close agreement is found between windtunnel measurements and the computed average and standard deviation of concentration in the wake of the building. Since the turbulent mass flux is equal to the covariance of velocity and concentration, we perform a detailed statistical analysis of these variables to gain insight into the dispersion process. In particular, the fact that turbulent mass flux in the streamwise direction is directed from the low to high levels of mean concentration (counter-gradient mechanism) is explained. The large vortical structures developing around the building are shown to play an essential role in turbulent mass transport.