Measurement of runaway electron beam (REB) is essential to investigate behavior of runaway electrons produced in nanosecond-pulse gas discharge. A Faraday cup is designed to measure the REB current in nanosecond-pulse discharge when the applied dV/dt is 75 kV/ns. The Faraday cup considers the impendence match with the oscilloscope and the design of the receiving part. The experimental results show that the measured REB current has a rise time of 348 ps and a full width at half maximum of 510 ps. The comparison of the measurement results by the Faraday cup and a REB collector confirm that the Faraday cup is able to measure REB current in nanosecond-pulse discharge. Furthermore, consecutive waveforms of the REB currents show stable results by using the designed Faraday cup. In addition, effects of the interelectrode gap, gas pressure, and cathode material on the REB current are investigated by the designed Faraday cup, and the measurement results provide characteristics of REB current under different conditions. The REB current decreases when the gap spacing or gas pressure increases. REB current increases with the cathode diameter. It indicates that the high-energy electrons are generated not only at the edge of the cathode but also on the side surface of the cathode.