The cry is a loud, high pitched verbal communication of infants. The very high fundamental frequency and resonance frequency characterize a neonatal infant cry having certain sudden variations. Furthermore, in a tiny duration solitary utterance, the cry signal also possesses both voiced and unvoiced features. Mostly, infants communicate with their caretakers through cries, and sometimes, it becomes difficult for the caretakers to comprehend the reason behind the newborn infant cry. As a result, this research proposes a novel work for classifying the newborn infant cries under three groups such as hunger, sleep, and discomfort. For each crying frame, twelve features get extracted through acoustic feature engineering, and the variable selection using random forests was used for selecting the highly discriminative features among the twelve time and frequency domain features. Subsequently, the extreme gradient boosting-powered grouped-support-vector network is deployed for neonate cry classification. The empirical results show that the proposed method could effectively classify the neonate cries under three different groups. The finest experimental results showed a mean accuracy of around 91% for most scenarios, and this exhibits the potential of the proposed extreme gradient boosting-powered grouped-support-vector network in neonate cry classification. Also, the proposed method has a fast recognition rate of 27 seconds in the identification of these emotional cries.