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With the advent of surface-enhanced Raman spectroscopy (SERS), dimers consisting of metal nanoparticles, as typical representatives of SERS substrates, have been extensively studied and applied. To achieve the optimal Raman enhancement, the extinction peak wavelength of the SERS-active dimer is matched with the excitation light to generate localized surface plasmon resonance (LSPR). For this purpose, the time-consuming numerical simulation is necessarily done to obtain the extinction peak wavelength. Therefore, a deep learning-based method for rapidly predicting the extinction peak wavelength of gold nanosphere dimer is proposed and demonstrated in this work. The maximum prediction error is 4.15%, and the average prediction error is 0.9%. The accuracy is sufficient for common SERS applications. Thus, this method offers a rapid and effective approach for designing SERS-active dimers and has the potential for application in other photonic nanostructure designs.