Collective cell migration is an essential phenomenon in many naturally occurring pathophysiological processes, as well as in tissue engineering applications. Cells in tissues and organs are known to sense chemical and mechanical signals from the microenvironment and collectively respond to these signals. For the last few decades, the effects of chemical signals such as growth factors and therapeutic agents on collective cell behaviors in the context of tissue engineering have been extensively studied, whereas those of the mechanical cues have only recently been investigated. The mechanical signals can be presented to the constituent cells in different forms, including topography, substrate stiffness, and geometrical constraint. With the recent advancement in microfabrication technology, researchers have gained the ability to manipulate the geometrical constraints by creating 3D structures to mimic the tissue microenvironment. In this study, we simulate the pore curvature as presented to the cells within 3D-engineered tissue-scaffolds by developing a device that features tortuous microchannels with geometric variations. We show that both cells at the front and rear respond to the varying radii of curvature and channel amplitude by altering the collective migratory behavior, including cell velocity, morphology, and turning angle. These findings provide insights into adaptive migration modes of collective cells to better understand the underlying mechanism of cell migration for optimization of the engineered tissue-scaffold design.