Conventional discharge (Townsend and streamer mechanisms) theories are not able to well explain the phenomenon in nanosecond-pulse discharges. Recently, much attention has been paid to the runaway breakdown due to high-energy electrons in nanosecond-pulse discharges, and some experimental data confirm that high-energy runaway electron beam is an important characteristic parameter for nanosecond-pulse discharges. In this paper, two designed collectors are used for detecting runaway electron beams in nanosecond-pulse discharges. These collectors are used to measure the runaway electron beams in discharges driven by a nanosecond-pulse generator with a pulse width of 3-5 ns and a rise time of 1.2-1.6 ns. The measuring principle of both two collectors is similar to that of Faraday cup, where high-energy electrons are collected by a metal cone, and converted into an electric signal that can be recorded by an oscilloscope. Furthermore, optimal designs of collectors are conducted in order to improve the impedance matching characteristics and to obtain better recording data. Using the above two collectors, characteristics of runaway electron beams are investigated. Experimental results show that runaway electron beams can be effectively measured by the collectors, and the optimized collector has a shorter time resolution and higher amplitude of the runaway electron beam current. When the applied voltage is 80 kV, the electron beam current can be measured with an amplitude of 160 mA and a full width at half maximum of less than 1 ns. In addition, experimental results with pulse sequences prove that the collectors have excellent reliability, and both the transient response and the time resolution are stable.