Infant cry detection is the most important part of automatic cry analysis and diagnosis for continuous infant health and wellness monitoring under various background sounds. Accurate and reliable detection of infant cry events in continuous audio recording is still a challenge in the presence of various mixed sounds and a mixture of sound sources. This paper presents an infant cry detection (Infant-Cry-Detect) method based on sound spectrograms and long short-term memory (LSTM) neural network architecture. The method is evaluated using diverse cry sound patterns and six background sounds in terms of standard performance metrics, model size, and processing time. On the large database having 120931 cry and 149766 non-cry test segments, evaluation results show that the LSTM-based Infant-Cry-Detect method achieved a sensitivity of 98.93%, specificity of 99.26%, and overall accuracy of 99.12% and outperforms other six machine learning based methods. The model has a size of 6.7 MB and a latency of 0.517 ms for processing 1 second audio.