A silent discharge plasma apparatus includes a dielectric member, a pair of electrodes opposed to each other across the dielectric member and an alternating-current source applying an alternating-current voltage between the electrodes and causing a discharge. A gas is supplied to a discharge space, where discharge occurs, and a plasma is produced. At least one of the electrodes includes a conductive power feeding thin film on the dielectric member. When the dielectric member is destroyed and an arc discharge develops between the electrodes, the power feeding thin film is eliminated or oxidized, and the arc discharge is stopped.