The continuous-variable quantum key distribution experimental system requires the randomness and speed of a Gaussian modulator. We present the hardware design for a Gaussian random number (GRN) generator based on the Box–Muller method, which can be implemented on a field-programmable gate array (FPGA). An external high-speed true random number generator application-specific integrated circuit (ASIC) is used to this end. The ASIC operates faster and more independently compared with other Gaussian algorithms based on a linear feedback shift register. The trigonometric and logarithmic functions are calculated using the nonuniform piecewise linear approximation. The calculation of the Gaussian random modulus and phase value is realized using this hardware. Compared with an arbitrary waveform generator, the GRN can be uploaded to a computer to estimate the security key rate. Furthermore, the GRN generator accurately provides a Gaussian probability density function that passes the Jarque–Bera inspection and Lilliefors tests. The proposed FPGA-based system is demonstrated to convert eight-channel 320-Mbps uniform random numbers to 40-MHz 16-bit GRN in real time. Finally, the control of the optical module and Gaussian modulation is realized via the FPGA-based outputs of four dual-channel, 16-bit, 1-giga samples per second digital-to-analog converters.