The purpose of this article is to explore the ways project-based firms respond to Government narratives of innovation. We focus on the narratives of innovation articulated by Government as part of industrial policy and the responses thereto by senior managers in project-based firms. Our research setting is a major project-based sector: UK construction. 45 narrative interviews were conducted in addition to the content analysis of the Government reports on construction innovation. We find that project-based firms respond to the Government narrative for the need for innovation to improve performance by developing and enhancing their innovative capabilities and generating their own narratives of innovation. The model developed shows how narrative interaction between the Government and project-based firm levels impact on meaning-making of innovation by (re)articulating collective identities, and shaping innovation strategies.