The lattice-Boltzmann method (LBM) is used to carry out a direct numerical simulation (DNS) of grid-generated turbulence with the view to improve comparison between experimental and numerical results on approximate isotropic turbulence. The grid is made up of four by four floating flat square elements in an aligned arrangement. The Reynolds number based on the Taylor microscale is about 40 at a distance of 70 times the separation between the elements downstream of the grid; this value is comparable to that of many experiments. While the results compare relatively well with existing experimental data on grid turbulence (grid made up of bars), they highlight the importance of the mesh resolution of the simulation and computational domain size in the decay of turbulence. For example, while a power-law decay could be identified, at least over a short distance, its decay exponent proves to be difficult to determine with good accuracy. This points out the need for simulations (and perhaps experiments too) where all scales are properly solved before conclusions can be drawn.