Cognitive diagnosis (CD) plays an important role in intelligent tutoring system. Computerized adaptive testing (CAT) is adaptive, fair, and efficient, which is suitable to large-scale examination. Traditional cognitive diagnostic test needs quite large number of items, the efficient and tailored CAT could be a remedy for it, so the CAT with cognitive diagnosis (CD-CAT) is prospective. It is more benefit to the students who live in the developing area without rich source of teaching and distance education is adopted there. Although many researchers pay attention to CD, some flaws exist because it is still in its infancy (Leighton at el.2007) and only a few researches of CD-CAT are gotten. In Tatsuoka's Q-matrix theory, it is wrong that the rows/columns could form a Boolean lattice. Based on Rule Space Model (RSM) and the Attribute Hierarchy Method (AHM), Formal Concept Analysis (FCA) is applied into CD-CAT. Concept lattices are served as the model of CD. The technology of item bank construction, item selection strategies in CD-CAT and estimation method are considered to design an initiatory and systemic CD-CAT, which diagnoses examinees on-line and offers remedial measure for examinees in time. The algorithms of constructing concept lattice for CAT, diagnosing examinees and offering the best remedial measure to examinees are discussed theoretically in detail. The result of Monte Carlo study shows that examinees' knowledge states are well diagnosed and the precision in examinees' abilities estimation is satisfied. (Contains 3 tables and 5 figures.)