An increased attention paid to “cognitive bugs behavior,” appears to lead to an increased research interests in diagnostic testing based on Item Response Theory（IRT）that combines cognitive psychology and psychometrics. The study of cognitive diagnosis were applied mainly to Paper-and-Pencil (P&P) testing. Rarely has it been applied to computerized adaptive testing CAT）, To our knowledge, no research on CAT with cognitive diagnosis has been conducted in China. Since CAT is more efficient and accurate than P&P testing, there is important to develop an application technique for cognitive diagnosis suitable for CAT. This study attempts to construct a preliminary CAT system for cognitive diagnosis.With the help of the methods for “ Diagnosis first, Ability estimation second ”, the knowledge state conversion diagram was used to describe all the possible knowledge states in a domain of interest and the relation among the knowledge states at the diagnosis stage, where a new strategy of item selection based-on the algorithm of Depth First Search was proposed. On the other hand, those items that contain attributes which the examinee has not mastered were removed in ability estimation. At the stage of accurate ability estimation, all the items answered by each examinee not only matched his/her ability estimated value, but also were limited to those items whose attributes have been mastered by the examinee.We used Monte Carlo Simulation to simulate all the data of the three different structures of cognitive attributes in this study. These structures were tree-shaped, forest-shaped, and some isolated vertices (that are related to simple Q-matrix). Both tree-shaped and isolated vertices structure were derived from actual cases, while forest-shaped structure was a generalized simulation. 3000 examinees and 3000 items were simulated in the experiment of tree-shaped, 2550 examinees and 3100 items in forest-shaped, and 2000 examinees and 2500 items in isolated vertices. The maximum test length was all assumed as 30 items for all those experiments. The difficulty parameters and the logarithm of the discrimination were drawn from the standard normal distribution N(0,1). There were 100 examinees of each attribute pattern in the experiment of tree-shaped and 50 examinees of each attribute pattern in forest-shaped. In isolated vertices, 2000 examinees are students come from actual case.To assess the behaviors of the proposed diagnostic approach, three assessment indices were used. They are attribute pattern classification agreement rate (abr.APCAR), the Recovery (the average of the absolute deviation between the estimated value and the true value) and the average test length (abr. Length).Parts of results of Monte Carlo study were as follows.For the attribute structure of tree-shaped, APCAR is 84.27%,Recovery is 0.17,Length is 24.80.For the attribute structure of forest-shaped, APCAR is 84.02%,Recovery is 0.172,Length is 23.47.For the attribute structure of isolated vertices, APCAR is 99.16%,Recorvery is 0.256,Length is 27.32.As show the above, we can conclude that the results are favorable. The rate of cognitive diagnosis accuracy has exceeded 80% in each experiment, and the Recovery is also good. Therefore, it should be an acceptable idea to construct an initiatory CAT system for cognitive diagnosis, if we use the methods for “Diagnosis first, Ability estimation second ” with the help of both knowledge state conversion diagram and the new strategy of item selection based-on the algorithm of Depth First Search