Low-power design has recently become very important especially in nanoelectronic VLSI circuits and systems. Functioning of circuits at ultra-low voltages leads to lower power consumption per operation. An efficient method is to separate the logic blocks based on their performance requirement and applying a specific supply voltage for each block. In order to prevent an enormous static current in these multi-VDD circuits, voltage level converters are essential. This study presents an energy-efficient and robust single-supply level converter (SSLC) based on multi-threshold carbon nanotube FETs (CNTFETs). Unique characteristics of the CNTFET device and transistor stacking are utilized suitably to reduce the power and energy consumption of the proposed LC. The results of the extensive simulations, conducted using 32nm CNTFET technology of Stanford University indicate the superiority of the proposed design in terms energy-efficiency and robustness to process, voltage and temperature variations, as compared to the other conventional and state-of-the-art LC circuits, previously presented in the literature. The results demonstrate almost on average 35%, 55%, 90% and 68% improvements in terms of delay, total power, static power and energy consumption, respectively.