To address the orbital angular momentum (OAM) recognition problem with imbalanced label distribution, a weighted extreme learning machine (WELM) recognition model based on the particle swarm optimization (PSO) algorithm is proposed. This model jointly optimizes the input weights and biases of WELM using PSO algorithm, enhancing the stability and robustness of WELM. A comparative analysis was conducted on the performance of the PSO-WELM model against support vector machine (SVM), deep learning (DL), and backpropagation artificial neural network (BP-ANN) models. Experimental results show that the PSO-WELM model can correctly identify minority-class and majority-class OAM beams under weak turbulence intensity. Under moderate turbulence intensity, all evaluation metrics of the PSO-WELM model outperform those of the comparative methods, demonstrating the feasibility and effectiveness of the model in recognizing imbalanced OAM beams.