In order to solve global environmental issues, we should construct stable circular product lifecycle systems. For this purpose, lifecycle design plays a crucial role; especially, it is necessary to determine lifecycle strategies at the early stage of lifecycle design. In the current practice of eco-design, for example, a designer increases the disassemblability of a product for recycling, although the product is shredded without disassembling. For avoiding such a situation and realizing stable circular product lifecycle systems, appropriate lifecycle strategies should be determined and implemented by designing both a product and its processes. This paper proposes a method for supporting design of a product lifecycle. The main approach is to support a designer to determine a lifecycle strategy by describing a lifecycle scenario, at early stage of lifecycle design. We define a representational scheme of the lifecycle scenario and develop the support system based on the idea of cognitive design process model so that a designer can examine various possibilities of lifecycle strategy. After this stage of lifecycle design, the product and its lifecycle processes should be designed so as to realize the strategy. In order to embody the strategy in the later stages, the system derives requirements for the product and process design. A case study indicates that the lifecycle scenario is successfully represented on a computer and a designer can easily determine lifecycle strategies by using this system.