The cyclic simple-shear behavior of soil-structure interfaces under different normal stresses is of great significance in theoretical analysis and engineering practices. A series of interface tests between gravel and steel was conducted under different normal stresses using a 3D large-scale simple-shear apparatus, and the influence of normal stress on the cyclic simple-shear behavior of the interface was explored in detail. The normal stress plays a crucial role in the magnitudes of the shear behavior of the interface, including deforming and sliding displacements, shear stress, reversible and irreversible normal displacement, and cyclic shear strength, while it has slight influence on the relationship pattern of shear behavior. Increased normal stress leads to increased deforming displacement at the first few shear cycles, accelerated reduction and decreased stabilized amplitude of deforming displacement. Enhanced normal stress also results in increased shear modulus, decreased shear modulus coefficient at the first a few shear cycles, increased stabilized shear stress and cyclic shear strength of the interface. In addition, larger normal stress results in larger irreversible normal displacement, smaller peak reversible normal displacement, smaller transition tangential displacement and transition stress ratio of the interface. The cyclic shear strength behaves well in accordance with Mohr-Coulomb criteria, regardless of normal stress. Perfect consistency exists in the stress ratio versus tangential displacement response and irreversible normal displacement versus shear work density response, independent of normal stress, and can be described using hyperbolic models. These consistency characteristics will significantly simplify the constitutive modelling of soil-structure interfaces.