BACE-1 and GSK-3β are potential therapeutic drug targets for Alzheimer's disease. Recently, both the targets received attention for designing dual inhibitors for Alzheimer's disease. Until now, only two-scaffold triazinone and curcumin have been reported as BACE-1 and GSK-3β dual inhibitors. Docking, molecular dynamics, clustering, binding energy, and network analysis of triazinone derivatives with BACE-1 and GSK-3β was performed to get molecular insight into the first reported dual inhibitor. Further, we designed and evaluated a naphthofuran series for its ability to inhibit BACE-1 and GSK-3β with the computational approaches. Docking study of naphthofuran series showed a good binding affinity towards both the targets. Molecular dynamics, binding energy, and network analysis were performed to compare their binding with the targets and amino acids responsible for binding. Naphthofuran series derivatives showed good interaction within the active site residues of both of the targets. Hydrogen bond occupancy and binding energy suggested strong binding with the targets. Dual-inhibitor binding was mostly governed by the hydrophobic interactions for both of the targets. Per residue energy decomposition and network analysis identified the key residues involved in the binding and inhibiting BACE-1 and GSK-3β. The results indicated that naphthofuran series derivative 11 may be a promising first-in-class dual inhibitor against BACE-1 and GSK-3β. This naphthofuran series may be further explored to design better dual inhibitors. Graphical abstract Naphthofuran derivative as a dual inhibitor for BACE-1 and GSK-3β.