A pneumatic vehicle tire has a carcass with at least one carcass ply. The surface of the carcass ply has an overlay made of an electrically conductive rubber mixture. The overlay extends continuously from an electrically conductive bead base to a superstructure and contacts the superstructure. A method for making a pneumatic vehicle tire includes the steps of making a carcass ply, covering a surface of the carcass ply with a continuous overlay made of an electrically conductive rubber mixture. The overlay contacts an electrically conductive bead base and the superstructure in the finished pneumatic vehicle tire.