To identify the vortex beams orbital angular momentum (OAM) with imbalanced labels, this paper proposes a derived model based on global cost SMOTE and deep extreme learning machine (DELM). Unlike typical machine learning methods, the proposed model can obtain the analytical expression of the mapping model. It avoids repeated parameter optimization, thus building a suitable model for time-varying engineering applications. In the data generation stage, the inverse matrix of covariance was used to remove the influence of dimensions, and the differences among samples within the same category were effectively measured. In the model selection stage, considering the transmission characteristics of light signals in atmospheric turbulence, the DELM was adopted to quantify the mapping relationship between light spots and labels. Then the FISTA algorithm was used to calculate the model’s analytical expression. Experiments were carried out on different intensity atmospheric turbulence data sets. The representative comparative methods include WELM and k-nearest neighbor. Experimental results show that the proposed method’s root mean square error (RMSE) achieves 0.2049 and 0.0894, which are superior to the comparison methods under different turbulence intensities. This proves that the proposed method can fully explore the characteristics of OAM spot collection and has a better recognition effect.