We present optical and near-infrared photometry and spectroscopy of the Type Ia SN 2003cg, which exploded in the nearby galaxy NGC 3169. The observations cover a period between 8.5 and +414d post-maximum. SN 2003cg is a normal but highly reddened Type Ia event. Its B magnitude at maximum Bmax=15.94+/-0.04 and {Delta}m15(B)obs=1.12+/-0.04 [{Delta}m15(B)intrinsic=1.25+/-0.05]. Allowing RV to become a free parameter within the Cardelli et al. (1989ApJ...345..245C) extinction law, simultaneous matches to a range of colour curves of normal SNe Ia yielded E(B-V)=1.33+/-0.11, and RV=1.80+/-0.19. While the value obtained for RV is small, such values have been invoked in the past, and may imply a grain size which is small compared with the average value for the local interstellar medium.