Continuous health status monitoring and advances in medical treatments have resulted in a significant increase of survival rate in critically ill infants admitted into Neonatal Intensive Care Units (NICUs). The quality of life and long-term health prospects of the neonates depend increasingly on the reliability and comfort of the monitoring systems. In this paper, we present the design work of a smart jacket for vital sign monitoring of neonates at a NICU. The design represents a unique integration of sensor technology, user focus and design aspects. Textile sensors, a reflectance pulse oximeter and a wearable temperature sensor were proposed to be embedded into the smart jacket. Location of the sensor, materials and appearance were designed to optimize the functionality, patient comfort and the possibilities for aesthetic features. Prototypes were built for demonstrating the design concept and experimental results were obtained from tests on premature babies at the NICU of Máxima Medical Centre (MMC) in Veldhoven, the Netherlands.