The behaviors of knowledge in designing human purposeful activities are studied. The knowledge flow and the efforts in making the knowledge more complete via competition,  i.e. the knowledge evolution in design are analyzed. The relations between innovation and design and the knowledge essentiality of innovation and design are discussed. The study reveals that design is based on existed knowledge and centered on new knowledge acquirement. The study also gives the incompleteness and competitiveness of knowledge in design. Since innovation has been identified as a basic driving force of the mode transformation of economic development,  the behaviors of knowledge should be important issues to be studied in design science.