Predicting medical insurance costs is a difficult task that requires calculating future medical expenses for individuals or groups based on their personal and medical data. Deep learning is the robust technique that can extract complicated relationships and patterns from huge and varied data sources. In this article, we suggest a novel deep learning model to predict the cost of medical insurance for a specific person based on their age, BMI, sex, number of children and smoking status. First, the Z-score pre-processing technique is employed to remove the noisy data. Then the metaheuristic optimization algorithm modified Fire Hawk Optimization (BFHO) is introduced for feature selection (FS) to select the most relevant features data, thus decreasing the number of features. Additionally, the dynamic chunk-based max pooling (DCMP) technique is employed to improve the pooling layer in CNN network and the improved golden eagle optimization (IGEO) approach is utilized to enhance the weight of the CNN network. Finally, this improved CNN is used for the prediction of medical insurance based on the medical dataset. The predictive performance of the proposed approach is systematically evaluated and benchmarked against several traditional methods, including the Improved Whale Optimization Algorithm (IWOA), Fire Hawk Optimization (FHO), Improved Manta Ray Foraging Optimization (IMRFO), Honey Badger Algorithm (HBA), and Binary Grey Wolf Optimizer (BGWO). The experimental results show that the proposed model is the best approach for the cost prediction of medical insurance.