The purpose of the study was to examine the importance of the authority structure in the design of a computer supported collaborative concept mapping system for elementary students. An experiment was implemented using ninety-six fifth- and sixth-grade Taiwanese students. The independent variable was the authority structure, which was assign, rotate, give, or open, and designed into the system. The dependent variables included the student performance in concept mapping, the student attitude toward collaborative concept mapping, and the quantity of knowledge related interactions by students. The findings suggest that the authority structure design results in different effects on elementary students.