A method for producing a capacitor includes: a dielectric body composed of basic alumina powder mixed with tungsten powder, interposed between a pair of electrodes disposed opposite to each other. The method includes the steps of: after a conductive alumina ceramic body has been formed by mixing the tungsten powder with the alumina powder, providing a pair of electrodes while interposing the conductive alumina ceramic body therebetween, and intermittently applying an electric current or voltage to the electrodes, high enough to break conductive paths formed in the conductive alumina ceramic body by the tungsten powder, so that the conductive ceramic body is converted to the dielectric body.