The paper presents a result of the direct numerical simulation with the lattice Boltzmann method which was conducted for quantitative prediction of turbulent broadband noise. For better prediction of broadband noise with high frequency, which is generally generated in high Reynolds number flows, not only high grid resolution is required for a flow simulation to capture very small eddies of the sound source inside the turbulent boundary layer, but also the computation of acoustic field is often needed. In such case, the direct simulation of flow field and acoustic field is straightforward and effective. In this study, the direct simulation with the lattice Boltzmann method was conducted for a flow around the NACA0012 airfoil with the Reynolds number of two hundred thousand. In order to efficiently simulate this high Reynolds number flow with the LBM, the multi-scale approach was introduced in conjunction with the Building-cube method, while keeping the advantage of the LBM with the Cartesian mesh. At the condition with angle-of-attack of 9 degrees, a laminar separation bubble arises on the suction surface near the leading-edge and the suction boundary layer downstream of it is turbulent due to the separated-flow transition. As a result, turbulent broadband noise is generated from the boundary layer over the airfoil with the separated-flow transition. In the paper, as for prediction of such broadband noise, the computed frequency spectrum of far-field sound is validated to agree with the experimental result. In addition, through the detailed analyses of turbulent properties of the turbulent boundary layer on the suction surface, the validity of the present direct numerical simulation is demonstrated.