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At the basic of introducing the connotation of the geographic space and the spatial differentiation within geographical science,this paper introduces two turns in geography space research with emphasis that are from natural space to social space and realistic space to virtual space.The research indicated that geographic space is a relatively clear concept,but its connotation is also in constant development,especially after human geography separated from the physical geography.The differences in studying geographical space among the three big branches of geographical science are enormous,among them,physical geography studies natural space,human geography studies social space and geographic information science studies geographic information space.The first turn of geography space research is from natural space to social space,which includes the turn of geographic space research focus,and the turn of space properties cognition.The second turn of geography space research is from realistic space to virtual space.The virtual space here includes both perceptional space and cyberspace.The turn of geography space research from nature to society reflects the synchrony with human development,and the turn of geography space research from reality to virtuality reflects the conformance with technical progress.