We have conducted multi-band (U, B, V, R, and I) polarimetric observations of the whole near-side of the Moon for phase angles between 22 degrees and 121 degrees with a spatial resolution of 1.1 km. A median grain size (< d >) map of the near-side regolith of the Moon has been constructed using our polarimetry. We find that < d > is a monotonically increasing function of selenographic latitude beta; < d > at vertical bar beta vertical bar similar or equal to 60 degrees is estimated to be up to 40% larger than that at the equator. At the same latitude, < d > is larger in the maria than in the highlands, confirming the initial findings of Shkuratov et al. The former is thought to be a result of reduced space weathering effects at high latitudes, where the flux of weathering agents such as micrometeoroids and solar wind particles is smaller. The latter probably indicates that the regolith material in the maria is more resistant to comminution by space weathering than is the material in the highlands. We also find that three photometric or polarimetric maturity indices-optical maturity, < d >, and the color ratio of parallel-component polarization (C-parallel to)-have different sensitivities on young small craters and rays of large craters. We present possible causes of these different sensitivities.