An electrostatic precipitator has a plurality of arrays of spaced parallel dust-collecting electrodes, and at least one array of spaced parallel discharge electrodes, each array of discharge electrodes is arranged between an adjacent pair of arrays of dust-collecting electrodes. Each array of dust-collecting electrodes and each array of discharge electrodes are arranged such that the faces of the dust-collecting and discharge electrodes are parallel to each other, and parallel to the flow direction of a gas to be treated. The spacing between the dust-collecting electrodes of an array of dust-collecting electrodes, and the spacing between the discharge electrodes of an array of discharge electrodes may be sequentially narrowed from the upstream side of the electrostatic precipitator to the downstream side of the electrostatic precipitator. The spacing between adjacent arrays of dust-collecting and discharge electrodes may also be sequentially narrowed from the upstream side of the electrostatic precipitator to the downstream side of the electrostatic precipitator.