In this study, by grafting a two-dimensional nanostructure of Borophene (B36) onto C20 fullerene, nanobuds with novel structures were designed and their stability was investigated using theoretical calculations based on density functional theory (DFT). In order to evaluate the stability and feasibility of forming these nanostructures, optimization of the geometric structure, vibrational spectrum (IR) analysis, and calculation of the binding energy were performed. The electronic properties of these nanobuds, including the energies of the HOMO and LUMO frontier orbitals and the energy gap (Eg), were determined using the density of states (DOS) spectrum. The results show that the designed nanobuds exhibit better electrical properties compared to the original molecules. The electron charge distribution analysis also showed that the nanobuds have a dipolar nature, such that the part containing B36 has a partial positive charge and the part consisting of C20 has a partial negative charge. Finally, in order to investigate the optical potential of these nanostructures, their linear and nonlinear optical properties were calculated and it was found that the B36 to C20 linkage leads to a significant improvement in their optical response. The feasibility of forming nanobuds from B36 and C20 and creating boron-carbon nanobuds was investigated in this research, and it was shown that these nanobuds, especially the B configuration, have suitable electronic, optical, and thermodynamic properties, which raises hopes for their application in photonics, optoelectronics, and nanotechnology.