Study on children’s number concept have occupied important position in the research on children’s cognitive development. However there are conflicts in this field. Susan Carey（2006, 2007, 2008）and colleagues have proposed a “knower-levels account” to describe the development of children’s number concept from a new aspect and also categorized children into different knower levels. Moreover, they proposed that successor function was the very basic reason that can be used to explain the difference between “subset-knowers” and “cardinal-principle knowers”. The present study was to explore the development of number concepts and examine whether the successor function were acquired step by step or all-or-none. 100 preschoolers of 2- to 5-year-olds, from two kindergartens in Hangzhou city, Zhejiang Province, participated in the study. The Give-N task was used to separate 2- to 5-year-olds into children who could give the right number of items for only a subset of the numerals in their count list (“subset-knowers”) and children who could give the right number for all numerals tested (“cardinal-principle knowers”). The results of the study showed: 1) The developmental pattern of preschoolers’ number concept was as follows: the cardinal number concept of 2- to 5-year-olds was developing continually. 3- to 4-year-old was the critical period of cardinal number concept. 2) From the view of “knower-levels account”, most 4-year-olds have already achieved the very high level of cardinal principle knower, while 2- to 3-year-olds were still on the pre-number level to the third level. Children of 2- to 3-year-old were the subset knowers. Chinese preschoolers could also be categorized into Carey’s knower levels and the result somehow supported Carey’s account. 3) From the view of “successor function”, performance on a series of novel numerical tasks supported the hypothesis that not only the cardinal-principle-knowers understood how counting implemented the successor function, but also subset-knowers understood the successor function in the condition of small sets. The successor function was acquired step by step, not all-or-none.