Noble gases possess extremely low reactivity because their valence shells are closed. However, previous studies have suggested that these gases can form molecules when they combine with other elements with high electron affinity, such as fluorine. Radon is a naturally occurring radioactive noble gas, and the formation of radon-fluorine molecules is of significant interest owing to its potential application in future technologies that address environmental radioactivity. Nevertheless, because all isotopes of radon are radioactive and the longest radon half-life is only 3.82 days, experiments on radon chemistry have been limited. Here, we study the formation of radon molecules using first-principles calculations; additionally, possible compositions of radon fluorides are predicted using a crystal structure prediction approach. Similar to xenon fluorides, di-, tetra-, and hexa-fluorides are found to be stabilized. Coupled-cluster calculations reveal that RnF6 stabilizes with Oh point symmetry, unlike XeF6 with C3V symmetry. Furthermore, relativistic effects are considered to calculate physical properties, such as bond length, bond angle, and vibrational spectra, and the results suggest that relativistic effects should be considered to describe properly many-electrons of Rn. The molecular stability of radon fluoride obtained through calculations may lead to advances in radon chemistry research.