A numerical simulation model was developed to predict the instantaneous concentration fluctuation of a plume and applied to stack-gas diffusion around a cubical building. The flow field, including an instantaneous velocity component, was predicted using the large eddy simulation (LES) method in the developed numerical model. Then, the instantaneous concentration fluctuation was predicted using the obtained unsteady flow field. Concentration was calculated using the finite difference method, in which the LES is expanded for concentration, and the puff method, in which small volumes of the tracer gas are divided and combined according to the calculation mesh sizes. In order to avoid numerical viscous effects, a puff method and finite difference method were applied separately in the regions near and far from the stack-gas release point, respectively. Then, the flow field around a cubical building and the diffusion of stack-gas, emitted from an elevated point source at an upstream position of the building, were calculated using the model mentioned above. Numerical calculation results were compared with those obtained in wind tunnel experiments in which concentration fluctuation was measured using high-response flame ionization detectors. Although there were some discrepancies in the flow field between the calculated results and those of wind tunnel experiments, e.g., the calculated windward length of a cavity region behind the building, the calculated mean velocity and turbulent intensity showed good agreement with those of the wind tunnel experiments. Furthermore, the calculated concentration fluctuation showed good agreement with that in the wind tunnel, not only regarding the features of fluctuating concentration signals, but also statistic quantities, viz., mean concentration, fluctuation intensity and high-concentration values.