This paper presents the results of horizontal cyclic direct shear tests at the reinforced soil interface of a four-way polypropylene geogrid reinforced sandy soil. The influence of normal stress and shear displacement amplitude on the shear stress, shear stiffness, and damping ratio of the reinforced soil interface are evaluated by varying the normal stress and shear displacement amplitude. Dynamic shear characteristics of reinforced soil interface under normal constant load were investigated by using a large dynamic straight shear apparatus. Peak interface strength increases with increasing amplitude of normal stress and shear displacement amplitude. The larger the normal stress and shear displacement amplitude, the fewer cycles are needed to attain peak interface strength. At low-magnitude normal stress levels, the peak shear stress and shear stiffness tend to stabilize after an initial increase during the cycling process, and the damping ratio decreases and then stabilizes with the increase in the number of cycles; whereas when the normal stress level is high, the peak shear stress and shear stiffness increase and then decrease during the cycling process and eventually stabilize, and the damping ratio decreases and then increases and finally stabilizes with the increase in the number of cycles. Moreover, under the same number of cycles, the corresponding shear stiffness decreases with an increase in shear displacement amplitude, while the damping ratio increases.