This paper presents an efficient method to generate quantized Gaussian noise. The proposed method is derived based on the fact that any signal received at a digital system should be quantized to several bits. On the contrary to the previous works that have focused on the precision of noise, the quantization process is taken into account in generating noise samples. As a result, the resultant bit-width of noise is significantly reduced and the computation complexity of generating Gaussian noise is also reduced by simplifying the interpolation process. The proposed architecture based on the inversion method is implemented on field-programmable gate array (FPGA) devices. Compared to the previous architecture based on the conventional inversion method, the proposed approach improves the throughput per slice by 460% while maintaining the statistical properties of Gaussian noise.