Optical and near-infrared (near-IR) observations of the Type Ic supernova (SN Ic) 2004aw are presented, obtained from −3 to +413 d with respect to the B-band maximum. The photometric evolution is characterized by a comparatively slow post-maximum decline of the light curves. The peaks in redder bands are significantly delayed relative to the bluer bands, the I-band maximum occurring 8.4 d later than that in B. With an absolute peak magnitude of −18.02 in the V band the SN can be considered fairly bright, but not exceptional. This also holds for the U through I bolometric light curve, where SN 2004aw has a position intermediate between SNe 2002ap and 1998bw. Spectroscopically SN 2004aw provides a link between a normal SN Ic like SN 1994I and the group of broad-lined SNe Ic. The spectral evolution is rather slow, with a spectrum at day +64 being still predominantly photospheric. The shape of the nebular O iλλ6300, 6364 line indicates a highly aspherical explosion. Helium cannot be unambiguously identified in the spectra, even in the near-IR. Using an analytical description of the light-curve peak we find that the total mass of the ejecta in SN 2004aw is 3.5–8.0 M⊙, significantly larger than that in SN 1994I, although not as large as in SN 1998bw. The same model suggests that about 0.3 M⊙ of 56Ni has been synthesized in the explosion. No connection to a GRB can be firmly established.