In this study, kink band formation behavior of an Al/Al2Cu eutectic alloy with a mille-feuille structure consisting of a hard Al2Cu phase and a soft Al phase was investigated under compression at room temperature. In-situ surface observations during compression tests revealed multiple micro kink-bands occurring simultaneously within a single lamellar colony. To analyze the formation behavior of micro kink-bands, the spatial distribution of the lamellar structure over a wide area of the specimen was quantitatively evaluated by performing image analysis using the Radon transform. The results showed that the micro kink-bands generated synchronously in one direction and rotated at a uniform angle. Such uniform and fine kink-bands are expected to contribute to the improvement of strength. To unravel the linkage between microstructure, kink band formation, and accompanying kink strengthening, an attempt was made to construct a model that predicts the spacing between micro kink-bands and critical stress for kinking from the features of the lamellar structure. The validity of the model to predict the spacing between kink bands was demonstrated by the experimental results.