Abstract: The space-time correlations are fundamental to the turbulence theory and have a broad application. In this paper, the authors perform direct numerical simulations of turbulent channel shear flows through the lattice Boltzmann method, and then study the space-time correlations of the velocity field. What's more, the authors investigate spacetime correlations of fluctuating velocities in porous wall-bounded turbulence, basing on the lattice Boltzmann equation which containing the Darcy-Brinkman-Forhheimer acting force term. On the one hand, the two-time correlations of velocities in porous wall-bounded shear flows are calculated and discussed. On the other hand, the author analyzes the space-time correlations of velocities in different porosity numbers and Darcy numbers in detail to investigate porous wall-bounded turbulent shear flows. It is found that there are elliptic curves on the iso-correlation contours that have a uniform preference direction and share a constant aspect ratio. Also, there are obvious di erences among the space-time correlations of velocities in different normal-wise positions, such as near-wall region, buffer layer, log-law region and outer layer. These findings suggest that the farther it is away from the wall, the more slender elliptic curves are in isocorrelation contours. The computed results suggest that the correlations are enhanced with the Darcy number decreasing and the porosity number increasing.