Computational aeroacoustics at low Mach number is challenging because of the comparative order of magnitudes between the acoustic perturbations and the numerical errors. The lattice Boltzmann method has been proven to be advantageous for aeroacoustics with a lower dissipation. The recursive and regularized LBM scheme (LBM-rrBGK), which has only been developed recently and tested in aeroacoustic problems, shows advantages over the traditional LBM-BGK. In this paper, results of computational aeroacoustics for low Mach number flow using rrBGK are presented. Two benchmark problems are tested, including the flow passing around a circular cylinder and the sound radiation of a cylindrical duct with uniform flow. The results are compared with either simulation, experiment or analytical results in the literature, and show a good agreement. Finally, the sound radiation directivity of the horn in the presence of mean flow is studied.