We present a study of the submillimeter ( submm ) emission of Distant Red Galaxies ( DRGs ) . The DRGs are selected by the criterion J - K > 2.3 , and are generally massive galaxies at redshifts higher than 2 , with red rest-frame optical colors . Using a deep SCUBA submm image of a field centred on the cluster MS 1054 { - } 03 , we obtain a statistical detection of the DRGs at redshift z = 2 - 3.5 , with an average 850 \mu m flux density of 1.11 \pm 0.28 mJy . The detection implies an average star formation rate ( SFR ) of 127 \pm 34 M _ { \odot } yr ^ { -1 } ( lensing corrected ) , assuming that the far-infrared ( FIR ) spectral energy distribution ( SED ) is well-described by a modified blackbody . The SFR derived from the submm agrees well with SFRs derived from SED fitting of optical-near-infrared data and average X-ray emission . Constant Star Formation models imply ages of 2Gyr , extinction A _ { V } = 2.4 mag , which is consistent with the FIR to rest-frame optical luminosity ratio of \sim 15 . DRGs are older and have lower SFRs relative to optical luminosity than ( ultra- ) luminous infrared galaxies , although their FIR luminosities are similar . The DRGs at 2 < z < 3.5 and the Extremely Red Objects ( I - K > 4 ) at 1 < z < 2 , which were also investigated , contribute 5.7 and 5.9 Jy deg ^ { -2 } respectively to the submm background . Simple estimates suggest that these populations contribute \sim 50 \% of the flux from sources with 0.5 < f _ { 850 } < 5 mJy , which is where the peak of energy is produced . We have therefore uncovered one of the most important populations of galaxies contributing to the sub-mm background .