We investigate the solar cycle variation of microwave and extreme ultraviolet (EUV) intensity in latitude to compare microwave polar brightening (MPB) with the EUV polar coronal hole (CH). For this study, we used the full-sun images observed in 17 GHz of the Nobeyama Radioheliograph from 1992 July to 2016 November and in two EUV channels of the Atmospheric Imaging Assembly (AIA) 193 A° and 171 A° on the Solar Dynamics Observatory (SDO) from 2011 January to 2016 November. As a result, we found that the polar intensity in EUV is anti-correlated with the polar intensity in microwave. Since the depression of EUV intensity in the pole is mostly owing to the CH appearance and continuation there, the anti-correlation in the intensity implies the intimate association between the polar CH and the MPB. Considering the report of Gopalswamy et al. (1999) that the enhanced microwave brightness in the CH is seen above the enhanced photospheric magnetic field, we suggest that the pole area during the solar minimum has a stronger magnetic field than the quiet sun level and such a strong field in the pole results in the formation of the polar CH. The emission mechanism of the MPB and the physical link with the polar CH are not still fully understood. It is necessary to investigate the MPB using high resolution microwave imaging data, which can be obtained by the high performance large-array radio observatories such as the ALMA project.