The purposes of this study are to confirm the accuracy of LES in modeling plume dispersion near and around a simple building model and to clarify the mechanism of the discrepancy in relation to the RANS computation. Simple LES modeling gives better results than RNG modeling of the distribution of concentration, although the difference for mean velocity is not so large. The horizontal diffusion of concentration is well reproduced by LES. This tendency is closely related to the reproduction of unsteady periodic fluctuation around the cube in LES.