In a high-voltage X-ray tube, which a cathode, which is held at negative high voltage during operating conditions, and an anode, which is held at positive high voltage during operating conditions, are disposed opposite each other in a vacuumized inner space, the anode being attached to an anode insulation element in such a way that the anode insulation element has a cylindrical shape or a shape tapering toward the anode and includes an opening to receive a high-voltage plug, and a pipe structure is provided by means of which a coolant is able to be supplied to the anode. This coolant can be in particular insulating oil or another electrically non-conducting liquid. The pipe structure can, for example, be integrated completely into the interior of the anode insulation element, but can also be integrated into the surface of the high-voltage plug. A solution is also possible in which the pipe structure is integrated into an intermediate element, which is situated between the anode insulation element and the high-voltage plug.