FreGrad is a lightweight and fast frequency-aware diffusion audio codec designed to generate realistic audio. Its framework includes discrete wavelet transform, frequency-aware expansion convolution, and a series of quality enhancement techniques for model generation. In experiments, FreGrad achieves a 3.7x speedup in training speed and a 2.2x speedup in inference speed compared to baseline models, while reducing model size by 0.6x (only 1.78 million parameters) without sacrificing output quality.