WASP-18 hosts a massive, very close-in Jupiter-like planet. Despite its young age (< 1 Gyr), the star presents an anomalously low stellar activity level: the measured log R'(HK) activity parameter lies slightly below the basal level; there is no significant time-variability in the log R'(HK) value; there is no detection of the star in the X-rays. We present results of far-UV observations of WASP-18 obtained with COS on board of Hubble Space Telescope aimed at explaining this anomaly. From the star's spectral energy distribution, we infer the extinction (E(B-V) approximate to 0.01 mag) and then the interstellar medium (ISM) column density for a number of ions, concluding that ISM absorption is not the origin of the anomaly. We measure the flux of the four stellar emission features detected in the COS spectrum (C II, C III, C IV, Si IV). Comparing the C II/C IV flux ratio measured for WASP-18 with that derived from spectra of nearby stars with known age, we see that the far-UV spectrum of WASP-18 resembles that of old (> 5 Gyr), inactive stars, in stark contrast with its young age. We conclude that WASP-18 has an intrinsically low activity level, possibly caused by star-planet tidal interaction, as suggested by previous studies. Re-scaling the solar irradiance reference spectrum to match the flux of the Si IV line, yields an XUV integrated flux at the planet orbit of 10.2 erg s(-1) cm(-2). We employ the rescaled XUV solar fluxes to models of the planetary upper atmosphere, deriving an extremely low thermal mass-loss rate of 10(-20) M-J Gyr(-1). For such high-mass planets, thermal escape is not energy limited, but driven by Jeans escape.