The electric potential of a transient laminar methane/air flame was studied in the pressure range of 0.2-2 MPa. The flame potential was measured with a thin electrode probe placed between an anode and a cathode. It was experimentally shown that the cathode and the anode potential drops are strongly influenced by the gas density and the geometry of electrodes. In order to explain the experimental results, we suggested that the electrode potential drop is related to the electrical properties of the flame in the quenching zones in the vicinity of electrodes. In our analysis the processes of electron attachment and detachment in flame quenching zone were taken into account. It was demonstrated that mainly the electron attachment process near the anode defines the anode potential drop. Because electron attachment significantly increases with pressure rise, at high pressure the electrical conductivity of the flame in quenching zones on anode and cathode is mainly defined by the ion drift. At these conditions, the anode potential drop tends to the cathode one. A simple analytical model of potential drop on the electrodes is proposed. A good correlation was found between experimental and numerical results.