A new algorithm based on the bald eagle search algorithm (NBES) is proposed to address the drawbacks of poor stability and low accuracy of the solution and poor robustness of the bald eagle search (BES) algorithm. First, the sine cosine optimization mechanism algorithm is fused in the search space selection stage of the BES algorithm, and the fused position update formula is constructed. Secondly, the inertial weight adaptive position update strategy is added in the search space prey phase of the BES algorithm. Finally, the position update formula is redefined by fusing the firefly optimization mechanism algorithm in the swoop phase of the BES algorithm. The performance of the NBES algorithm is verified by 11 standard test functions, and the experiments show that the NBES algorithm outperforms the BES algorithm in terms of search accuracy, convergence speed, and robustness. To verify the practical application value of the new algorithm, the hyperparameter learning rate in the convolutional neural network (CNN) is optimized by using the NBES algorithm, and the optimized image classification model is used in medical image pathology classification prediction, and the experiments show that the classification accuracy of the optimized CNN model is improved by 9%.