Effective disaster prediction is essential for disaster management and mitigation. This study addresses a multi-classification problem and proposes the Neural-XGBoost disaster prediction model (N-XGB), a hybrid model that combines neural networks (NN) for feature extraction with XGBoost for classification. The NN component extracts high-level features, while XGBoost uses gradient-boosted decision trees for accurate predictions, combining the strengths of deep learning and boosting techniques for improved accuracy. The N-XGB model achieves an accuracy of 94.8% and an average F1 score of 0.95 on a real-world dataset that includes wildfires, floods and earthquakes, significantly outperforming baseline models such as random forest, Support vector machine and logistic regression 85% accuracy. The balanced F1 scores for wildfires 0.96, floods 0.93, and earthquakes 0.96 demonstrate the model's robustness in multi-class classification. The Synthetic Minority Oversampling Technique (SMOTE) balances datasets and improves model efficiency and capability. The proposed N-XGB model provides a reliable and accurate solution for predicting disasters and contributes to improving preparedness, resource allocation and risk management strategies.