The cognitive mechanisms of knowledge representation, memory establishment, and learning are fundamental issues in understanding the brain. A basic approach to studying these mental processes is to observe and simulate how knowledge is memorized by little children. This paper presents a simulation tool for knowledge acquisition and memory development for young children of two to five years old. The cognitive mechanisms of memory, the mathematical model of concepts and knowledge, and the fundamental elements of internal knowledge representation are explored. The cognitive processes of children’s memory and knowledge development are described based on concept algebra and the object-attribute-relation (OAR) model. The design of the simulation tool for children’s knowledge acquisition and memory development is presented with the graphical representor of memory and the dynamic concept network of knowledge. Applications of the simulation tool are described by case studies on children’s knowledge acquisition about family members, relatives, and transportation. This work is a part of the development of cognitive computers that mimic human knowledge processing and autonomous learning.