A baseline correction method based on low-rank constraint and penalized least squares (LRPLS) is proposed. This paper comprehensively considers the fitted baseline's fidelity to the interferogram and its own smoothness by using the penalized least squares model. At the same time, the low-rank and sparse prior constraint conditions of the effective interferogram and noise are introduced to build a regularization framework combing the low-rank matrix recovery and penalized least squares, and the solution is carried out by an augmented Lagrangian multiplier based iterative optimization algorithm. The experiments on the data of Chang'e-1 interference imaging spectrometer (IIM) show that the proposed method can retain effective information of the interferogram while removing the baseline. Compared with existing baseline correction methods, the proposed method has better stability and anti-noise ability. In addition, the recovered hyperspectral image significantly improves after baseline correction, which has high practical significance for improving the data quality of IIM.