The paper systematically analyzes the implementation process of the parallel factor analysis (PARAFAC) method decompose matrix data. As example, The three dimensional fluorescence spectra of the water samples taken from the lake were analyzed by PARAFAC. According to the distribution of the core matrix elements, the core consistency, the degree of similarity between the model spectra and the original spectra, the physical meaning of the proposed decomposition components, the number of components was determined. Then the corresponding PARAFAC model was established. The components of the fluorescence material components dissolved in water samples can be decomposed by this PARAFAC model.