The Gamma-Ray Burst 031203 at a redshift z=0.1055 revealed a highly reddened Type Ic Supernova, SN 2003lw, in its afterglow light. This is the third well established case of a link between a long-duration GRB and a type Ic SN. The SN light curve is obtained subtracting the galaxy contribution and is modelled together with two spectra at near-maximum epochs. A red VLT grism 150I spectrum of the SN near peak is used to extend the spectral coverage, and in particular to constrain the uncertain reddening, the most likely value for which is E_{G+H}(B-V) about 1.07 +/- 0.05. Accounting for reddening, SN 2003lw is about 0.3 mag brighter than the prototypical GRB-SN 1998bw. Light curve models yield a 56Ni mass of about 0.55 solar mass. The optimal explosion model is somewhat more massive (ejecta mass about 13 solar mass) and energetic (kinetic energy about 6 times 10^52 erg) than the model for SN 1998bw, implying a massive progenitor (40 - 50 solar mass). The mass at high velocity is not very large (1.4 solar mass above 30000 km/s, but only 0.1 solar mass above 60000 km/s), but is sufficient to cause the observed broad lines. The similarity of SNe 2003lw and 1998bw and the weakness of their related GRBs, GRB031203 and GRB980425, suggest that both GRBs may be normal events viewed slightly off-axis or a weaker but possibly more frequent type of GRB.