Constant composition codes (CCCs) are a special class of constant-weight codes. They include permutation codes as a subclass. The study and constructions of CCCs with parameters meeting certain bounds have been an interesting research subject in coding theory. A bridge from zero difference balanced (ZDB) functions to CCCs with parameters meeting the Luo-Fu-Vinck-Chen bound has been established by Ding (IEEE Trans. Information Theory 54(12) (2008) 5766-5770). This provides a new approach for obtaining optimal CCCs. The objective of this letter is to construct two classes of ZDB functions whose parameters not covered in the literature, and then obtain two classes of optimal CCCs meeting the Luo-Fu-Vinck-Chen bound from these new ZDB functions.