Semi-analytic models of galaxy formation are powerful tools to study the evolution of a galaxy population in a cosmological context. However, most models overpredict the number of lowmass galaxies at high redshifts and the colors of model galaxies are not right in the sense that low-mass satellite galaxies are too red and centrals are too blue. The recent version of the L-Galaxies model by Henriques et al. (H15) is a step forward to solve these problems by reproducing the evolution of stellar mass function and the overall fraction of red galaxies. In this paper we compare the two model predictions of L-Galaxies ( the other is Guo et al., G13) to SDSS data in detail. We find that in the H15 model the red fraction of central galaxies now agrees with the data due to their implementation of strong AGN feedback, but the stellar mass of centrals in massive halos is now slightly lower than what is indicated by the data. For satellite galaxies, the red fraction of low-mass galaxies (log M+/M-circle dot < 10) also agrees with the data, but the color of massive satellites (10 < log M-*/M-circle dot < 11) is slightly bluer. The correct color of centrals and the bluer color of massive satellites indicate that quenching in massive satellites is not strong enough. We also find that there are too many red spirals and less bulge-dominated galaxies in both H15 and G13 models. Our results suggest that additional mechanisms, such as more minor mergers or disk instability, are needed to slightly increase the stellar mass of the central galaxy in massive galaxies, mainly in the bulge component, and bulge dominated galaxies will be quenched not only by minor mergers, but also by some other mechanisms.