Near-boundary Brownian motion is a classic hydrodynamic problem of great importance in a variety of fields, from biophysics to micro-/nanofluidics. However, owing to challenges in experimental measurements of near-boundary dynamics, the effect of interfaces on Brownian motion has remained elusive. Here a computational study, using molecular dynamics simulation and a newly developed Green-Kubo relation for friction at the liquid-solid interface, unambiguously reveals that the t-3/2 long-time decay of the velocity autocorrelation function of a Brownian particle in bulk liquid is replaced by a t-5/2 decay near a boundary. A general breakdown of traditional no-slip boundary condition has been observed at short-time scales and it has been shown that this breakdown has a profound impact on the near-boundary Brownian motion. These results demonstrate the potential of Brownian motion in the nearby liquid-solid interface to be used as advanced sensing applications.