Abstract: Up to now, the academic community has conducted sufficient researches on river classification and segmentation, but there is still a lack of systematic analysis and unified understanding. In this paper, based on three river morphology elements of watershed basin, drainage network and mainstream channel, independent rivers and non-independent rivers as a method of river classification were firstly proposed. Then, comprehensive lists were ranked respectively for 55 independent rivers worldwide and for non-independent tributaries or drainage networks of the Yangtze River while a pedigree was summarized for all rivers or drainages of the Yangtze River. Finally, the river morphology science was preliminarily established and discussed. The research results were as follows: (1) Independent rivers follow principle of estuary priority while complexity of river morphology can be classified into compound watershed or drainage and complex mainstream channel. Based on approximate 0.5 power correlationship between river length and river basin area, 3 characteristic indexes of river morphology, namely river featured length, compositive river basin area and river curved indicator were proposed. (2) By index of compositive river basin area, the top 10 rivers worldwide are Rivers of Amazon, Nile, Congo, Ob, Yenise, Yangtze, Lena, Mississppi, Niger and Amur. (3) The river morphology science should include cornerstone researches of river classification, stream-order gradation and river segmentation, and researches on morphology of river channel. Study on river classification and establishment of river morphology science enable to fill researching gap between sciences of river geomorphology and fluvial processes, and gradually form researching system on river features of geometry-kinematics-dynamics corresponding to river morphology, fluvial processes and river mechanics.