Detection of infant cries in noisy environments such as homes, hospitals and clinics is vital to determine the reason of baby's cry. Also, It is crucial to classify the detected cry signals into normal or pathological cries especially in the first months of the baby life. This paper proposes a deep learning automatic infant cry detection and classification system under noisy conditions. It classifies the detected cry signals into normal , asphyxia and deaf cry signals . The overall system is composed of two stages ; cry detection stage and cry classification stage. In first stage, features(Mel-frequency cepstrum coefficients MFCC) are extracted from audio signals collected from a daily life dataset and passed into a 2D-two layers convolutional neural network(2DCNN) to be classified into cry and non cry signals. In second stage , a 2D-three layers CNN is used to classify cry signals collected from dataset with cry segments only into Normal (N) , Asphyxia (A) and Deaf (D) signals according to extracted MFCC features . In first stage, Testing results show that the cry detection system reaches an accuracy of 99.59 % for classifying the signals into cry and non-cry . In second stage, Due to the lack of pathological cry signals datasets that are collected in noisy environments, we added different levels of white noise to the training dataset. This way, we were able to get more realistic results. In particular, our cry classification system achieves accuracy of 91.3% ,94.2% , 95.07 % (under white noise) with signal-to-noise ratio(SNR) of 5db, 10db and 15db, respectively.