The work aims to explore the important role of children's cognitive development theory in the design of campus square space, propose design strategies to adapt to children's growth space, and provide children with a harmonious and friendly growth environment. Based on the theory of children's cognitive development, following the four basic cognitive concepts of schema, assimilation, adaptation and balance, this work analyzes the existing children's public space from the dimensions of space and color cognition. It is believed that children's space should have environmental comfort, consciousness privacy, space exploration and other attribute characteristics, while dull color, rough material and single function are the main problems of children's space at present. The theory is introduced into the space design of the campus square in combination with the above spatial attribute requirements as a whole, starting from the three levels of form cognition, color cognition and function cognition, and the design research is carried out around children's spontaneous behavior, social tendency and thinking variability, which reflects the diversified needs and interdisciplinary nature of children's space construction, effectively improves the children's growth environment, and can provide practical reference for the design of children's growth space.