To identify the types of heavy metal stress on crops, corn leaves under heavy metal stress of copper (Cu) and plumbum (Pb) were selected as the research object. The hyperspectral data of corn leaves were obtained by ASD Field-Spectrometer. The original spectral data were processed by fractional differential (FD), and feature bands were extracted by competitive adaptive reweighted sampling method (CARS). Finally, multi-layer perceptron (MLP), K-nearest neighbor (KNN) and support vector machine (SVM) were used to distinguish the spectra of stressed leaves. The FD-CARS-MLP model constructed by the optimal MLP was selected to distinguish the spectral information of corn growth copper and plumbum pollution. The results showed that the FD-CARS-MLP model was better than the traditional methods in spectral discrimination of stressed leaves. The accuracy of the FD-CARS-MLP model could reach more than 98% in all test sets, and the accuracy of fractional differential discrimination of 0.1 and 0.2 orders could reach more than 99%. Corn leaves at the seedling stage and heading stage were selected for the feasibility test of the FD-CARS-MLP model. It was proved that the FD-CARS-MLP model had higher accuracy and more stability in identifying the spectral data of corn leaves under heavy metal stress, which could provide technology and methods for monitoring different heavy metal stresses of cereal crops.