A functional feature extraction method based on rational function approximation for hyperspectral image (HSI) classification is proposed. In digital imagery, the spectral information of a pixel can be regarded as a 1-D signal. An HSI is composed of these 1-D signals arranged in a certain spatial structure. According to the functional characteristic of hyperspectral data, 1-D signals can be approximated by a linear combination of basis functions. Thus, a joint rational basis function system (JRBFS) based on class adaptivity is here first built for an HSI by adaptive Fourier decomposition (AFD). Second, the functional representations (FRs) and corresponding reconstructed spectral curves are obtained by decomposing the original spectral information in a JRBFS. Furthermore, the functional spectral-spatial features are extracted on the basis of FRs by an edge-preserving filtering method, FR-EPFs. Finally, the functional spectral-spatial features are used for HSI classification by SVM. Experimental results for five commonly used HSI data sets demonstrate the effectiveness and advantages of the proposed method FR-EPFs.