The purposes of this study were (1) to construct a test for measuring cognitive developmental abilities of children according to J. S. Bruner´s theory, (2) to investigate the relationships between grades and cognitive abilities of children (3) to explore the differences between the cognitive abilities in city children and rural children, and (4) to discuss the connection between the levels of the intelligence and cognitive abilities. 320 subjects (160 boys and 160 girls) in grades three to six were selected from two elementary schools in Miau-Li and Taipei city. Each subject was tested through a self-compiled test with ten questions, three items in each. Each question was presented tin he order of symbolic item, pictoral item, and then manually operation alreal materials, in order to prevent learning experience bias. The results were as follows: (1) The cognitive developmental ability of "enactive representation" was found to be the highest one in all grade levels of children, the "iconic representation" the next, and the "symbolic representation" the lowest. Besides, the higher grade the child went into, the more "symbolic representation" was used, comparing to the "iconic representation" and "enactivereprentation" (2) The cognitive abilities of city children were superior to those of rural children. (3) The Chidren with high intellgence were superior to those with low intellgence in all three stages of cognitive development. It was concluded that there are close relationships among cognitive developmental ability of children, grade, cultural background, and intelligence.