Plant-specific TCP transcription factors play vital roles in the controlling of growth, development, and the stress response processes. Extensive researches have been carried out in numerous species, however, there hasn’t been any information available about TCP genes in sweet potato (Ipomoea batatas L.). In this study, a genome-wide analysis of TCP genes was carried out to explore the evolution and function in sweet potato. Altogether, 18 IbTCPs were identified and cloned. The expression profiles of the IbTCPs differed dramatically in different organs or different stages of leaf development. Furthermore, four CIN-clade IbTCP genes contained miR319-binding sites. Blocking IbmiR319 significantly increased the expression level of IbTCP11/17 and resulted in a decreased photosynthetic rate due to the change in leaf submicroscopic structure, indicating the significance of IbmiR319-targeted IbTCPs in leaf anatomical morphology. A systematic analyzation on the characterization of the IbTCPs together with the primary functions in leaf anatomical morphology were conducted to afford a basis for further study of the IbmiR319/IbTCP module in association with leaf anatomical morphology in sweet potato.