The mean color of globular cluster (GCs) systems in early-type galaxies (ETGs) is, in general, bluer than the integrated color of field stars in their host galaxies. Recently, Goudfrooij & Kruijssen (2013) reported that even red GCs in the ETGs show bluer colors than their host field stars and suggested the different initial mass function (IMF) for red GCs and field stars to explain the observed offset in color. Here we suggest an alternative scenario that explains the observed color offsets between red GCs in ETGs and the field stars in the parent galaxies without invoking to the variation of the IMF. We find that the inclusion of second-generation (SG) helium-enhanced populations in the model fully explains the observed color offset between red GCs and field stars in the host galaxies. We have also tested the effect of the IMF slope on our models, but the effect is relatively small compared to the effect of the SG population. Our new model suggests that, in order to explain far-UV strong metal-rich GCs in M87 and the observed color offset between metal-rich GCs and the field stars in ETGs simultaneously, the inclusion of the SG populations with enhanced helium abundance is a more natural solution than the model that only adopted variations in the IMF.