Nanosecond-pulse discharge can produce low-temperature plasma with high electron energy and power density in atmospheric air, thus it has been widely used in the fields of biomedical science, surface treatment, chemical deposition, flow control, plasma combustion and gas diode. However, some phenomena in nanosecond-pulse discharge cannot be explained by traditional discharge theories (Townsend theory and streamer theory), thus the mechanism of pulsed gas discharge based on runaway breakdown of high-energy electrons has been proposed. Generally, the generation and propagation of runaway electrons are accompanied by the generation of X-ray. Therefore, the properties of X-ray can indirectly reveal the characteristics of high-energy runaway electrons in nanosecond-pulse discharges. In this paper, in order to explore the characteristics of runaway electrons and the mechanism of nanosecond-pulse discharge, the temporal properties of X-ray in nanosecond-pulse discharge are investigated. A nanosecond power supply VPG-30-200 (with peak voltage 0200 kV, rising time 1.2-1.6 ns, and full width at half maximum 3-5 ns) is used to produce nanosecond-pulse discharge. The discharge is generated in a tube-to-plane electrode at atmospheric pressure. Effects of the inter-electrode gap, anode thickness and position on the characteristics of X-ray are investigated by measuring the temporal X-ray via a diamond photoconductive device. The experimental results show that X-ray in nanosecond-pulse discharge has a rising time of 1 ns, a pulse width of about 2 ns and a calculated energy of about 2.310-3 J. The detected X-ray energy decreases with the increase of inter-electrode gap, because the longer discharge gap reduces the electric field and the number of runaway electrons, weakening the bremsstrahlung at the anode. When the inter-electrode gap is 50 mm, the discharge mode is converted from a diffuse into a corona, resulting in a rapid decrease in X-ray energy. Furthermore, both X-ray energies measured behind the anode and on the side of discharge chamber decrease as anode thickness increases. The X-ray energy measured on the side of the discharge chamber is one order of magnitude higher than that measured behind the anode, which is because the anode foil absorbs some X-rays when they cross the foil. In addition, the X-ray energy behind the anode significantly decreases with the increase of the thickness of anode aluminum foil. It indicates that the X-ray in nanosecond-pulse discharge mainly comes from the bremsstrahlung caused by the collision between the high-energy runaway electrons and inner surface of the anode foil. Therefore, increasing the thickness of the anode foil will reduce the X-ray energy across the anode film.