  The star-formation rates and the stellar masses of the host galaxies of AGNs at high-redshifts are keys to understanding the evolution of the relation between the mass of the spheroidal component of a galaxy and the mass of its central black hole. We investigate the host galaxies of 31 AGNs with spectroscopic redshifts between 2 and 4 found in the deep Chandra surveys of the GOODS fields with the ACS images. The sample can be divided into 17 ``extended'' AGNs and 14 ``compact'' AGNs based on the concentration parameter defined as the difference between the aperture magnitudes with 0.07" and 0.25" diameter. We derive upper limits of the UV luminosities of the host galaxies of the ``compact'' AGN sample, and upper and lower limits of the UV luminosities of the host galaxies of the ``extended'' AGN sample.These limits are consistent with the knee of the luminosity function of the Lyman Break Galaxies (LBGs) at z=3, suggesting moderate star-formation rates, less than 40 Msolar/yr, in the host galaxies of the AGNs at 2<z_sp<4 without correcting the dust extinction. By combining the limits of the UV luminosities with the observed K-band magnitudes for the ``extended'' AGNs, we derive the upper and lower limits of the stellar masses of their host galaxies. The derived upper limits on the stellar masses range from 10^10 Msolar to 10^12 Msolar. The upper limits imply that the Mbulge-MBH relation of the high-redshift AGNs is different from that of the galaxies in the nearby universe or the average Eddington ratio of the high-redshift AGNs is higher than that of low-redshift AGNs with lower-luminosity. 
Host Galaxies of the High-redshift AGNs in the GOODS Fields