Abstract: Geographical science studies order degree and its changes of the earth surface system in a definite spatial and temporal scales. Contemporary geography is facing several serious challenges: (1) the complexity of the earth surface system is very difficult to be described quantitatively; (2) the change speed of relationship between human and the earth oversteps human ability for identifying and forecasting warning; (3) there exists a contradiction between fuzzy characteristics of the earth surface system of and exact demand for scientific value; (4) acute competition exists between geography and other scientific disciplines. Geography development might have the following tendencies in the 21st century: (1) geography study pays more attention to humanism; (2) interface study would be a hot point for physical geography study; (3) global study would be a big issue for geography study; (4) geography would pay more concern to ecological security; (5) mountain research would become an important field. For accelerating geography development, the author gives the suggestions as follows: (1) bring up a number of geographical thinkers and strategists; (2) assembling all useful methods from other disciplines for geography and creating new geographical methodology; (3) seeking quantitative methodology to suit different demands in different development levels; (4)focusing geography study on big subjects concerning with human future.