The number of data points of digitally recorded spectra have been limited by the number of multi-channel detectors employed, which sometimes inhibits the precise characterization of spectral peak shape. Here we describe a methodology to increase the number of data points as well as the signal-to-noise (S/N) ratio by applying Bayesian super-resolution in the analysis of spectroscopic data. In our present method, first the hyperparameters for the Bayesian super-resolution are determined by a virtual experiment imitating actual experimental data, and the precision of the super-resolution reconstruction is confirmed by the calculation of errors from the ideal values. For validation of the super-resolution reconstruction of spectroscopic data, we applied this method to the analysis of Raman spectra. From 200 Raman spectra of a reference Si substrate with a data interval of about 0.8 cm-1, super-resolution reconstruction with a data interval of 0.01 cm-1 was successfully achieved with the promised precision. From the super-resolution spectrum, the Raman scattering peak of the reference Si substrate was estimated as 520.55 (+0.12, -0.09) cm-1, which is comparable to the precisely determined value reported in previous works. The present methodology can be applied to various kinds of spectroscopic analysis, leading to increased precision in the analysis of spectroscopic data and the ability to detect slight differences in spectral peak positions and shapes.