We trap neutral ground-state rubidium atoms in a macroscopic trap based on purely electric fields. For this, three electrostatic field configurations are alternated in a periodic manner. The rubidium is precooled in a magneto-optical trap, transferred into a magnetic trap, and then translated into the electric trap. The electric trap consists of six rod-shaped electrodes in cubic arrangement, giving ample optical access. Up to 105atoms have been trapped with an initial temperature of around 20 microkelvin in the three-phase electric trap. The observations are in good agreement with detailed numerical simulations.