Three-dimensional numerical simulations for air flow around a surface-mounted cube are carried out using the standard κ-ε model and Large Eddy Simulation (LES) with similar boundary con- ditions. The results of LES agree fairly well with the experimental results. The shortcomings of the κ-ε model are examined precisely using both the experimental data from the wind tunnel tests and the numerical data given by LES. The inaccuracies are concerned with the expression for evaluating the turbulence production under Eddy Viscosity Model and the unsuccessful reproduction of Karman's vortex street.