<p>Transfer learning algorithms can transform prior knowledge into linearization knowledge to model nonlinear systems. However, the linearization knowledge-based models tend to diverge in the process of knowledge linearization due to the neglected information of higher-order terms. To overcome this problem, a second-order knowledge filter transfer learning algorithm (SOFTLA) is developed for modeling nonlinear systems. First, a knowledge transformation strategy is introduced to transform the linearization source knowledge into comprehensive knowledge containing first-order and second-order terms. Compared with the original knowledge, the transformed source knowledge with second-order term can prevent information loss during the knowledge linearization. Second, a knowledge filter algorithm is proposed to eliminate the useless information in the source knowledge. Subsequently, a suitable filter gain is designed to reduce the cumulative error in knowledge updating process. Third, a model adaptation mechanism is designed to enable effective knowledge transfer by updating the structure and parameters of the target model simultaneously. Subsequently, the adaptability of the source knowledge is enhanced to facilitate learning tasks in the target domain. Finally, a benchmark problem and several practical industrial applications are presented to validate the superiority of SOFTLA. The experimental discussions illustrate that SOFTLA can obtain obvious advantages over contrastive methods.</p>