High alumina (HA) mare basalts play unique roles in understanding the heterogeneity of lunar mantle. Their presence was confirmed by the Apollo and Luna samples, and their remote sensing identification was implemented using HA sample FeO, TiO2 and Th concentration constraints. This study selected the surfaces with ~0.5% rock abundance as windows into HA basalts identification. The lithology of these rock pixels was first classified based on thorium maps from the Lunar Prospector and major element oxide products from Diviner data onboard the Lunar Reconnaissance Orbiter (LRO). Then, the LRO Diviner Al2O3 (~11 wt%) concentration constraint was applied in the mare basalt rock pixels across the Moon. The mare-highland mixtures were distinguished from HA basalt rocks based on the positive linear relationships between Al2O3 and Mg# in the adjacent pixels for four impact vector directions away from each candidate HA pixel. These HA basalts rock pixels identified by this study indicate that HA basalts are concentrated locally in South Pole-Aitken (SPA) basin, Schiller-Schickard region and 13 maria such as southern and northern Oceanus Procellarum, central Humorum, Tranquillitatis, Fecunditatis and Serenitatis, northern Imbrium and southern Nubium, but are seldom found in Mare Moscoviense and Orientale regions on the farside. Detailed investigations in Mare Fecunditatis found that fifteen HA basalt units or patches could be confidently identified. These HA basalts have the total area and volume of <77,658 km2 and <54,301 km3, and the maximum depth and thickness of 1147 m and 1062 m respectively. In addition, analyses of the HA rocks indicated that the HA basalts are discontinuous and have variable thicknesses.