Functional design is regarded as a design activity primarily aimed at clarifying customer needs, and developing the functional architecture and solution concepts for a system under development. Existing functional design approaches are mainly focused on how to assist designers in searching for solution principles for desired products, which, however, do not adequately take into account the interactions between a smart system under development and its environment, and cannot explicitly represent the complex functional logic of the system, resulting in that they cannot effectively assist designers in the functional design of smart systems. Therefore, this paper proposes a scenario-integrated approach for functional design of smart systems to address the above issues. Based on the concept of scenario in software engineering, the proposed approach explicitly elaborates how to employ scenarios to express subjective customer needs and how to generate the functional architectures and the corresponding solution concepts through a structured process. The functional design of the automated doors-unlocking system of a smart vehicle is employed to illustrate the proposed approach, which also demonstrates that the proposed approach is suitable for functional design of smart systems.