Collective coupling of multiple atoms with a cavity mode produces two normal modes that are separated in energy by Vacuum Rabi splitting. We show that the normal mode excitation of the cavity-atom system can be suppressed by coupling a control laser to the atomic system from free space. The control laser splits the normal mode of the cavity-atoms system and opens two excitation channels. The destructive quantum interference between the two channels renders the cavity-atoms system opaque to the light coupled to the cavity-atom system. We demonstrate suppression of the normal mode excitation by the destructive quantum interference in an experiment using cold Rb atoms confined in an optical cavity.