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This paper proposes a new CAD model for the design of lattice material components. The CAD model better captures the user’s design intent and provides a dual-scale framework to represent the geometry and material distribution. Conventional CAD model formats based on B-Rep generate millions of data files, which also makes design intent and material information missing. In the present work, a new shape-material model for lattice material components is proposed. At the macroscopic scale, a compact face-based non-manifold topological data structure is proposed to express the lattice shape-material information without ambiguity. At the microscopic scale, implicit function is adopted for the representation of lattice material components. Numerical experiments verify that the proposed CAD model provides a powerful support for design intent with minor space costs. Meanwhile, the representation method supports solid modeling queries of geometric and material information on each scale.