The electrical characteristics of a filamentary dielectric barrier discharge (DBD) are studied experimentally and numerically. The DBD system which has parallel plate electrodes geometry is powered by a 50 Hz power supply and operated at atmospheric air. A dynamic electric circuit model considering the discharge region and the non-discharge region being connected by a surface resistance is proposed. Simulation using this model is shown to fit the experimentally measured QV diagram satisfactorily. The effects of the air gap distance and the dielectric surface on the discharge behavior are then investigated. It is found that the surface resistivity of the dielectric is one of the important parameters governing the discharge behavior.