A shielding structure for a circuit on a circuit board has a conductive box member for enclosing a region of the surface of the circuit board requiring shielding. The edge defining the open side of the conductive box member has a conductive rib protruding therefrom. A conductive pattern member is formed on the surface of the circuit board in the same shape as the edge of the conductive box member so as to encircle the region requiring shielding. The conductive box member is fastened on the circuit board by screws so as to cause the conductive rib to bite into the conductive pattern member and establish good electrical connection therewith. A conductive sheet can be inserted between the conductive box member and the conductive pattern member to further enhance the shielding effect.