Raman spectroscopy has advantages of rapid response, non-contact, less detection restrictions and high selectivity, which make it widely used in many fields of production and life. However, the actual measured Raman spectra contain varying degrees of baseline drift, which seriously affects the validity and accuracy of spectral analysis. In order to solve the issues that the final baseline is underestimated in the no peak region and the height of peaks might be overestimated in existing baseline correction methods, we propose a novel correction algorithm, which is named locally symmetric reweighted penalized least squares (LSRPLS). Based on asymmetrical least squares, the method works by iteratively adjusting weights of the difference between the fitted baseline and the original signal, introducing the idea of local symmetric weighting by a softsign function. The algorithm is applied to the simulated and the actual Raman spectra to correct the baseline drifting. The results show that the LSRPLS algorithm can not only correct different types of baselines, but also has good advantages in accuracy and stability compared with the existing baseline correction methods. In addition, after baseline correction, the distribution of samples in principal component spaces becomes concentrated, and the classification accuracy of the model is significantly improved. This indicates that the LSRPLS algorithm can retain the spectral information effectively while removing the baseline, which provides a basis for further analysis of Raman spectroscopy.