A novel method is developed to study the charging of a conducting surface covered by a thin dust layer in plasma. The potential profile in the dust layer and the floating potential of the surface underneath are measured directly by embedding conducting wires in the dust and connecting the wires to a measurement plate outside the vacuum chamber, where a Trek non-contacting electrostatic voltmeter measures the floating potential of the measurement plate. Laboratory experiments are carried out to study plasma charging of a conducting plate covered by lunar dust simulant, JSC-1A. The results show that the plate potential is dependent on both the ambient plasma condition and the dust layer thickness. The current balance condition controls the floating potential of the dust surface while the dust layer acts as a capacitor and controls the potential of the plate with respect to the dust surface. Hence, a dust covered conducting plate will be charged more negatively than a clean plate.