The analysis of elements in drilling cuttings using laser-induced breakdown spectroscopy (LIBS) technology can not only provide information about underground formations, optimize the drilling process, but also enhance the safety and economy of drilling. Affected by the complex drilling environment, the LIBS of drilling cuttings generally exhibits a relatively severe baseline drift phenomenon, while the existing baseline correction methods are prone to issues such as baseline underestimation or overestimation. Therefore, an improved adaptive penalized least-squares baseline correction method is proposed. Based on the asymmetric penalized least-squares algorithm, the tanh function is introduced to automatically adjust the weight matrix according to the peak height of the spectral signal, and a smooth parameter automatic adjustment strategy is designed by utilizing the difference and standard deviation between the spectral data and the estimated baseline to balance the conflict between the smoothness and fidelity of the spectral data during baseline correction. Verification was conducted on both simulated spectra and the measured LIBS of drilling cuttings. The results indicate that the proposed method has lower root mean square error (RMSE) values on simulated spectra with different noise levels, and improves the quantitative analysis accuracy of elements on the measured LIBS of cuttings with the R2 values of 0.992 6, 0.993 0, 0.968 4, 0.969 1, and 0.977 4 for five elements, namely Si, Ca, Mg, Al, and Fe, respectively, all exceeding 0.96. It can effectively promote the element analysis of drilling cuttings in complex oil and gas environments using laser-induced breakdown spectroscopy technology.