In the analysis of trace substances in hair by Surface-Enhanced Raman Spectroscopy (SERS), the characteristic peaks of hair are coupled with the background peaks of the substrate. In the case of coupling, the background peaks are mistakenly identified as the characteristic peak of hair, resulting in the identification error of the analyte to be tested. In addition, the strong background peak has a masking interference on the weak characteristic peak in hair. Therefore, the background peak deduction is an important way to solve the above problems. However, the conventional peak deduction method always leads to serious distortion of the surrounding peaks. In this paper, a Gaussian mixture model is proposed. The model not only characterizes the SERS signal but also makes each characteristic peak independent of the other, and does not interfere with the adjacent peaks in the process of peak deduction, which realizes the deduction of interference peaks and ensures the micro distortion of adjacent peaks. The core problem of the Gaussian mixture model is the solution of model parameters. In this paper, wavelet transform and conjugate gradient methods are proposed to solve the model’s initial parameter problem and optimal solution problem. The wavelet transforms fully extracts the subtle feature information of the signal by mapping the detailed information of the amplified SERS signal and takes the feature information as the initial parameter of the model. The conjugate gradient method is an iterative optimization method, and the model parameters are iteratively optimized. The final convergence result is the optimal solution of the model parameters. In summary, the two methods can accurately establish the Gaussian mixture model, and the single Gaussian function is the characteristic peak of the SERS signal, and the peak shape of the two methods is consistent. The deduction of background peak should include the extraction of effective data, model establishment, and peak deduction. The effective data extraction is to detect the blank and sampled substrate in the same position, thus obtaining a set of SERS signals. The model was established to characterize the SERS signal of the sampled substrate by the Gaussian mixture model, which multiple Gaussian functions can express. Finally, the SERS signal of the sampled substrate was identified by the characteristic peaks of the blank substrate, and the characteristic peaks with similar peak shapes and the same peak position can be deducted. The results show that when the variance ratio is the smallest, the peak position, peak width, and peak intensity of the Gaussian mixture model are the same as those of the hair SERS signal. At this time, the Gaussian mixture model can accurately characterize the information of SERS signal of hair. In seven groups of hair peak deduction experiments, of the hair SERS signal background peak deduction rate reached 50%~100%, while the hair characteristic peak wasalso effectively extracted. The model was used to identify tramadol in the rapid analysis of real hair samples.