Fuzzy neural networks (FNNs) hold the advantages of knowledge leveraging and adaptive learning, which have been widely used in nonlinear system modeling. However, it is difficult for FNNs to obtain the appropriate structure in the situation of insufficient data, which limits its generalization performance. To solve this problem, a data-knowledge-driven self-organizing FNN (DK-SOFNN) with a structure compensation strategy and a parameter reinforcement mechanism is proposed in this article. First, a structure compensation strategy is proposed to mine structural information from empirical knowledge to learn the structure of DK-SOFNN. Then, a complete model structure can be acquired by sufficient structural information. Second, a parameter reinforcement mechanism is developed to determine the parameter evolution direction of DK-SOFNN that is most suitable for the current model structure. Then, a robust model can be obtained by the interaction between parameters and dynamic structure. Finally, the proposed DK-SOFNN is theoretically analyzed on the fixed structure case and dynamic structure case. Then, the convergence conditions can be obtained to guide practical applications. The merits of DK-SOFNN are demonstrated by some benchmark problems and industrial applications.