In order to improve the accuracy of simulation in which k-ε EARSM turbulent model was employed, the influence of grids thickness Δy on the turbulent variables in flow field around building was researched. Coupled with real data of Texas Tech University experimental building, Δy as the main parameter was studied in the numerical wind tunnel simulation. Equation of k-ε EARSM and simplified equation of Δy were analyzed and deduced. Quasi-steady State Marching-on-in-time Approximation technology was employed to simulate the average flow in five working conditions, in which y is 0.001m, 0.005m, 0.01m, 0.05m, and 0.1m, respectively. And based on the results, the comparison of characteristic of flow around building, turbulent kinetic energy coefficient, fluctuating pressure coefficient along axis and mean pressure coefficient was conducted. The results indicate that very small Δy will make fluid with high Reynolds number penetrate into near-wall zone, and the calculation stability worsens; on the other side, very large Δy will lower simulated accuracy of main variable results in the turbulent region near the cornice with high Reynolds number. Accordingly, Δy near the wall ranging from 0.01m～0.05m meets the requirements for accuracy and stability, then the experiential formula of Δy upper limit is given.