Asphyxia is a respiratory injury that leads to a serious damage for infants. Early detection of asphyxia using Artificially Intelligent technology helps in reducing infant mortality rate when compared to traditional medical diagnosis, which is time consuming. In this paper, we propose a novel method through generating weighted prosodic features combined with acoustic features to form a merged feature matrix to classify asphyxiated baby crying effectively. The weights of the prosodic features are trained at the frame level with labeled data and can be optimized using deep learning approach with neural networks. The novel merged feature matrix is established with both acoustic and weighted prosodic features. The matrix has good ability to capture the diversity of variations within infant cries, especially for asphyxiated samples. Our method has the benefits of keeping the robustness and resolution of the classification model simultaneously. The effectiveness of this approach is evaluated on Baby Chillanto Database. Our method yields a significant reduction of 3.11%, 3.23%, and 1.43% absolute classification error rate compared with the results using single acoustic features, single prosodic features, and both acoustic and prosodic features, respectively. The testing accuracy in our method reaches 96.74%, which outperforms all other related studies on asphyxiated baby crying classification.