Quantum Key Distribution is the process of using quantum communication to establish a shared key between two parties. It has been demonstrated the unconditional security and effective communication of quantum communication system can be guaranteed by an excellent Gaussian random number generator with high speed and an extended random period. In this paper, we propose to construct the Gaussian random number generator using Field-Programmable Gate Array (FPGA) which is able to process large data in high speed. We also compare three algorithms ofGRNgeneration: Box-Muller algorithm, polarization decision algorithm, and central limit algorithm. We demonstrate that the polarization decision algorithm implemented inFPGArequires less computing resources and also produces a high-quality Gaussian random number, through the null hypothesis test.