We have computed the evolution of the rest-frame B-band luminosity function (LF) for bulge and disk-dominated galaxies since z=1.2. We use a sample of 605 spectroscopic redshifts with I_{AB}<24 in the Chandra Deep Field South from the VIMOS-VLT Deep Survey, 3555 galaxies with photometric redshifts from the COMBO-17 multi-color data, coupled with multi-color HST/ACS images from the Great Observatories Origin Deep Survey. We split the sample in bulge- and disk-dominated populations on the basis of asymmetry and concentration parameters measured in the rest-frame B-band. We find that at z=0.4-0.8, the LF slope is significantly steeper for the disk-dominated population (alpha=-1.19 pm 0.07) compared to the bulge-dominated population (alpha=-0.53 pm 0.13). The LF of the bulge-dominated population is composed of two distinct populations separated in rest-frame color: 68% of red (B-I)_{AB}>0.9 and bright galaxies showing a strongly decreasing LF slope alpha=+0.55 pm 0.21, and 32% of blue (B-I)_{AB}<0.9 and more compact galaxies which populate the LF faint-end. We observe that red bulge-dominated galaxies are already well in place at z~1, but the volume density of this population is increasing by a factor 2.7 between z~1 and z~0.6. It may be related to the building-up of massive elliptical galaxies in the hierarchical scenario. In addition, we observe that the blue bulge-dominated population is dimming by 0.7 magnitude between z~1 and z~0.6. Galaxies in this faint and more compact population could possibly be the progenitors of the local dwarf spheroidal galaxies.