High-performance organic friction modifiers (OFMs) added to lubricating oils are crucial for reducing energy loss and carbon footprint. To establish a new class of OFMs, we measured the friction and wear properties of N-(2,2,6,6-tetramethyl-1-oxyl-4-piperidinyl)dodecaneamide referred to as C12Amide-TEMPO. The effect of its head group chemistry, which is characterized by a rigid six-membered ring sandwiched by an amide group and a terminal free oxygen radical, was also investigated with both experiments and quantum mechanical (QM) calculations. The measurement results show that C12Amide-TEMPO outperforms the conventional OFMs of glyceryl monooleate (GMO) and stearic acid, particularly for load-carrying capacity, wear reduction, and stability of friction over time. The friction and wear reduction effect of C12Amide-TEMPO is also greatly superior to those of C12Ester-TEMPO and C12Amino-TEMPO, in which ester and amino groups replace the amide group, highlighting the critical role of the amide group. The QM calculation results suggest that, in contrast to C12Ester-TEMPO, C12Amino-TEMPO, and the conventional OFMs of GMO and stearic acid, C12Amide-TEMPO can form effective boundary films on iron oxide surfaces with a unique double-layer structure: a strong surface adsorption layer owing to the chemical interactions of the amide oxygen and free radical with iron oxide surfaces, and an upper layer owing to the interlayer hydrogen-bonding between the amide hydrogen and free radical or between the amide hydrogen and oxygen. Moreover, the intralayer hydrogen-bonding in each of the two layers is also possible. We suggest that in addition to strong surface adsorption, the interlayer and intralayer hydrogen-bonding also increases the strength of the boundary films by enhancing the cohesion strength, thereby resulting in the high tribological performance of C12Amide-TEMPO. The findings in this study are expected to provide new hints for the optimal molecular design of OFMs.