Baseline drift is an important issue in spectral analysis (e.g., infrared, Raman, and laser-induced spectroscopy). Most common methods for baseline correction perform poorly in high noise, complex baselines, and overlapping peaks. To solve this problem, we proposed an adaptive extended Gaussian peak derivative reweighted penalised least squares (agdPLS) method for removing baseline drift from spectra. The method added extended Gaussian peaks to spectra, added derivative terms for spectral and baseline differences during iterations, and adaptively adjusted penalty coefficients λ. Experiments with simulated and measured spectra for methane and ethane were carried out to compare the performance of the different methods. agdPLS performed better than the other methods, with more accurate baseline estimation in low- and high-noise situations. Especially when the spectrum contained high noise, complex baselines and overlapping peaks, the agdPLS method performed significantly better than other methods. Moreover, agdPLS was computationally efficient. Results of actual spectral experiments showed that the proposed agdPLS method could be effective for baseline correction of spectra which, in turn, improved qualitative and quantitative spectral performances.