Lung diseases associated with alveoli, such as acute respiratory distress syndrome, have posed a long-term threat to human health. However, an in vitro model capable of simulating different deformations of the alveoli and a suitable material for mimicking basement membrane are currently lacking. Here, we present an innovative biomimetic controllable strain membrane (BCSM) at an air–liquid interface (ALI) to reconstruct alveolar respiration. The BCSM consists of a high-precision three-dimensional printing melt-electrowritten polycaprolactone (PCL) mesh, coated with a hydrogel substrate—to simulate the important functions (such as stiffness, porosity, wettability, and ALI) of alveolar microenvironments, and seeded pulmonary epithelial cells and vascular endothelial cells on either side, respectively. Inspired by papercutting, the BCSM was fabricated in the plane while it operated in three dimensions. A series of the topological structure of the BCSM was designed to control various local-area strain, mimicking alveolar varied deformation. Lopinavir/ritonavir could reduce Lamin A expression under over-stretch condition, which might be effective in preventing ventilator-induced lung injury. The biomimetic lung-unit model with BCSM has broader application prospects in alveoli-related research in the future, such as in drug toxicology and metabolism.