We report results from a 50 ks XMM-Newton observation of the dust-reddened broad-line quasar FTM 0830+3759 (z=0.413) selected from the FIRST/2MASS Red Quasar survey. For this AGN, a very short 9 ks Chandra exposure had suggested a feature-rich X-ray spectrum and HST images revealed a very disturbed host galaxy morphology. Contrary to classical, optically-selected quasars, the X-ray properties of red (i.e. with J-Ks> 1.7 and R-Ks> 4) broad line quasars are still quite unexplored, although there is a growing consensus that, due to moderate obscuration, these objects can offer a unique view of spectral components typically swamped by the AGN light in normal, blue quasars. The XMM-Newton observation discussed here has definitely confirmed the complexity of the X-ray spectrum revealing the presence of a cold (or mildly-ionized) absorber with Nh ~10^{22} cm^-2 along the line of sight to the nucleus and a Compton reflection component accompanied by an intense Fe K emission line in this quasar with a Lum(2-10) ~5 x 10^{44} erg/s. A soft-excess component is also required by the data. The match between the column density derived by our spectral analysis and that expected on the basis of reddening due to the dust suggests the possibility that both absorptions occur in the same medium. FTM 0830+3759 is characterized by an extinction/absorption-corrected X-ray-to-optical flux ratio alphaox = -2.3, that is steeper than expected on the basis of its UV luminosity. These findings indicate that the X-ray properties of FTM 0830+3759 differs from those typically observed for optically-selected broad line quasars with comparable hard X-ray luminosity.