This paper introduces support vector machines in deep learning algorithms that can model and analyze cross-cultural teaching and knowledge bases. Wavelet functions are used instead of traditional functions to perform deep learning on training samples. Finally, the learning ability of the support vector machine is improved by the wavelet kernel function to complete the effective instruction of higher education teachers to develop students’ intercultural competence. The results show that the accuracy rate of the intercultural teaching level of the deep learning algorithm proposed in this paper reaches up to 99.25%, and the results of the intercultural ability performance of the higher vocational students are excellent, which shows that the method of this paper can improve the intercultural teaching ability of foreign language teachers and strengthen the intercultural knowledge training of students in higher vocational institutions.