This study purposed for diagnosing students’ cognitive state and change by Bayesian Inference Network Model in the fraction problem solving. Bayesian Network is an annotated directed graph that encodes probabilistic relationships among distinctions of interest in an uncertain-reasoning problem. Bayesian Inference Network Model is appropriate for cognitive diagnosis as it illustrates the relationship among cognitive variables and provides the probability a student to have the cognitive attributes. Also it can use the prior knowledge and personal belief which the study of cognitive psychology and curricula are developed. This paper presented cognitive process model of fraction problem solving and estimated each student cognitive state and cognitive change between pretest and posttest, The experimental group and control group were compared to test the effect of cognitive diagnosis by Bayesian Inference Network Model. They were different significantly. The change of cognitive state between pretest and posttest was tested in individual level and group level. Implications for the analysis of cognitive state in the individual level and group level in the context of instruction and assessment are discussed.