We propose a ground-state cavity-mediated cooling scheme for a trapped atom, which is in the Λ configuration and confined inside a high-finesse optical cavity, using a standing-wave cooling laser. The carrier transition can be prohibited by placing the atom at the node of the cavity field, and the blue-sideband transition can be simultaneously eliminated by exploiting quantum interference via tuning the frequency of the cooling laser. As a consequence, the ground-state cooling for the trapped atom can be achieved. Moreover, we numerically demo...