The controversy on ‘design science’ since the end of 19_th century was reviewed. An analysis of the change of the cognition and idea of design in the ‘period of pre-industrial design’, ‘period of industrial design’ and ‘period of post-industrial design’ was given, especially in the period of industrial design. The change came following a rapid increase of the production capacity in meeting material needs. In fact, when the capacity could not meet material needs the competition of industrial production is scale expanding priority. Until an extremely expanding led to an overcapacity and a series of social problems the competition became to innovation priority. The change of competition paradigm changes the cognition and idea of design: from a rational and systematic design which ensured the large scale production of material products and followed the principles of material transformation into a creation leading design which tracks the desire of people in pursuing new things and better life which must meet simultaneously the material needs, psychological needs and social needs. Which design can make the innovation successful is decided by competition, not only the competition in market but also the competition in the social development process. The problem now is not that one who can or cannot design but the design with or without competitiveness. China is now on the way of mode transformation of economic development and it is very important to push forward the study of design science and make clear the change in design cognition and idea. The concepts of ‘competitive design’ and ‘inheriting design’ are suggested in the paper and discussed.