Summary: In this paper color image compression using a fuzzy Hopfield-model net based on rough-set reasoning is created to generate optimal codebook based on Vector Quantization (VQ) in Discrete Wavelet Transform (DWT). The main purpose is to embed rough-set learning scheme into the fuzzy Hopfield network to construct a compression system named Rough Fuzzy Hopfield Net (RFHN). First a color image is decomposed into 3-D pyramid structure with various frequency bands. Then the RFHN is used to create different codebooks for various bands. The energy function of RFHN is defined as the upper- and lower-bound fuzzy membership grades between training samples and codevectors. Finally, near global-minimum codebooks in frequency domain can be obtained when the energy function converges to a stable state. Therefore, only 32/N pixels are selected as the training samples if a 3N-dimensional color image was used. In the simulation results, the proposed network not only reduces the consuming time but also preserves the compression performance.