Anthocyanins, which have important biological functions and have a beneficial effect on human health, notably account for pigmentation in purple-fleshed sweet potato tuberous roots. Individual regulatory factors of anthocyanin biosynthesis have been identified; however, the regulatory network of anthocyanin biosynthesis in purple-fleshed sweet potato is unclear. We functionally determined that IbMYB340 cotransformed with IbbHLH2 in tobacco and strawberry receptacles induced anthocyanin accumulation, and the addition of IbNAC56a or IbNAC56b caused increased pigmentation. Furthermore, we confirmed the interaction of IbMYB340 with IbbHLH2 and IbNAC56a or IbNAC56b via yeast two-hybrid and firefly luciferase complementation assays; these proteins could form a MYB340-bHLH2-NAC56a or MYB340-bHLH2-NAC56b transcriptional complex to regulate anthocyanin biosynthesis by binding to the IbANS promoter rather than the IbUFGT promoter. Furthermore, it was found by a transient expression system in tobacco leaves that IbMYB44 could decrease anthocyanin accumulation. Moreover, the interaction of IbMYB44 with IbMYB340 and IbNAC56a or IbNAC56b was verified. This result suggested that IbMYB44 acts as a repressor of anthocyanin in sweet potato. The repressor IbMYB44 affected anthocyanin biosynthesis by competitively inhibiting the IbMYB340-IbbHLH2-IbNAC56a or IbMYB340-IbbHLH2-IbNAC56b regulatory complex formation. Overall, the present study proposed a novel regulatory network whereby several vital TFs play key roles in regulating anthocyanin biosynthesis, and it provides strong insight into the potential mechanism underlying anthocyanin biosynthesis in sweet potato tuberous roots with purple color.