Automated health monitoring and alert system development is a demanding research area today. Most of the currently available monitoring and controlling medical devices are wired which limits freeness of working environment. Wireless sensor network (WSN) is a better alternative in such an environment. Neonatal intensive care unit is used to take care of sick and premature neonates. Hypothermia is an independent risk factor for neonatal mortality and morbidity. To prevent it an automated monitoring system is required. In this Letter, an automated neonatal health monitoring system is designed using sensor mobile cloud computing (SMCC). SMCC is based on WSN and MCC. In the authors' system temperature sensor, acceleration sensor and heart rate measurement sensor are used to monitor body temperature, acceleration due to body movement and heart rate of neonates. The sensor data are stored inside the cloud. The health person continuously monitors and accesses these data through the mobile device using an Android Application for neonatal monitoring. When an abnormal situation arises, an alert is generated in the mobile device of the health person. By alerting health professional using such an automated system, early care is provided to the affected babies and the probability of recovery is increased.