Surface-enhanced Raman spectroscopy (SERS) holds remarkable potential for the rapid and portable detection of trace molecules. However, the analysis and comparison of SERS spectra are challenging due to the diverse range of instruments used for data acquisition. In this paper, a spectra instrument transformation framework based on the penalized functional regression model (SpectraFRM) is introduced for cross-instrument mapping with subsequent machine learning classification to compare transformed spectra with standard spectra. In particular, the nonparametric forms of the functional response, predictors, and coefficients employed in SepctraFRM allow for efficient modeling of the nonlinear relationship between target spectra and standard spectra. In the leave-one-out training and test of 20 analytes across four instruments, the results demonstrate that SpectraFRM can provide interpretable corrections to peaks and baseline spectra, leading to approximately 11% error reduction, compared with original spectra. With an additional feature extraction step, the transformed spectra outperform the original spectra by 10% in analytes identification tasks. Overall, the proposed method is shown to be flexible, robust, accurate, and interpretable despite varieties of analytes and instruments, making it a potentially powerful tool for the standardization of SERS spectra from various instruments.