Computerized adaptive test for cognitive diagnosis(CD_CAT) is the product of the theory and method of cognitive diagnosis(CD) and Computerized adaptive test(CAT), and is a new developing modern measurement field. The research on the selection strategy in CAT is always a focus topic internationally. While there are few reports about the research on the selection strategy in CD_CAT, and there are less reports about the research on initial items selection strategy in CD_CAT. Methods: Using Monte Carlo simulation, this paper compared five selection strategies and 2 initial items selection strategies with HO-DINA model. Conclusions: Different initial items selection methods and different selection strategies can affect the accurate of diagnosis and the precision of ability estimation. Totally, To two initial items selection strategies, the T-matrix method suggested in this paper is better than the traditional stochastic method; To five selection strategies, SL_GDI method is the best; and among the pairwise of initial items selection strategies and selection strategies, the pair of T-matrix method and SL_GDI is the best match.