•Graphyne is explored as a carrier for daunorubicin drug.•Graphyne possess significant therapeutic potential as a drug carrier.•For visual explanation of different excited-states, PET process and electron-hole theory are used. In this research, for the first time; graphyne is investigated as a carrier for delivery of anticancer drug, daunorubicin. The effectiveness of graphyne as a carrier, is explored with the help of calculations of some physiochemical properties such as band-gap, dipole-moment, and chemical-reactivity-descriptors for daunorubicin drug, graphyne carrier and daunorubicin-graphyne complex by using Density Functional Theory (DFT) method. Daunorubicin has significant antimitotic and cytotoxic activity as it can form complex with DNA by intercalation. The nature of interactions between graphyne and daunorubicin complex are clarified through noncovalent-interaction (NCI) analysis, which demonstrated that Vander-Waals force of interactions are present between the graphyne carrier molecule and daunorubicin drug. Daunorubicin drug will easily off-load at the target point as weak forces are present between drug and graphyne carrier. Frontier-molecular-orbital-analysis explained that how charge-transferred from daunorubicin to graphyne in complex formation process. The charge-transfer process is further studied by charge-decomposition-analysis (CDA). The calculations at excited-state indicated that the λmax of daunorubicin-graphyne complex show red-shift of 91 nm. PET process is also studied for excited-states of daunorubicin-graphyne complex with the help of electron-hole theory and it revealed that fluorescence-quenching process will occur in complex molecule. The process of fluorescence-detection is very useful for systematic delivery of daunorubicin drug at target site for the perfect treatment. Moreover, the effect of + 1 and −1 charge-state on graphyne molecule and its complex with daunorubicin is also investigated. Overall, the calculations suggested that graphyne could be utilized as an efficient carrier for targeted-delivery of daunorubicin.