CP-nets (conditional preference networks) is a simple and intuitive graphical tool for representing conditional preference statements over the values of a set of variables. It has been a studying hotspot in artificial intelligence recently. The algorithm of strong dominance with respect to any binary-valued CP-nets has not been given; preferences completeness of CP-nets have not been studied by anyone, This paper makes a study of completeness and consistency of CP-nets by designing a strong dominance algorithm. First, by constructing induced graph of CP-nets and studying its properties, the study solves the problem of strong dominance with respect to any binary-valued CP-nets by Warshall algorithm to get the transitive closure of flip relation. Second, by solving the preference number of three kinds of CP-nets (separeble-structured, chain-structured, tree-structured), the study gives preferences incompleteness theorem and counting number formula of separeble condition preference networks. Finally, the study deals with consistency problem, and consistency judgment theorem and algorithm are given. The method not only solves some difficult problems proposed by Boutilier and Goldsmith, but also deepens the basic theory researching of CP-nets.