As an advanced composite material with a flexible structure, cord-rubber composite has the advantages of high strength, high modulus, and lightweight, widely used in aerospace and other fields. Compared with our previous work, we focus on the effects of three kinds of overlap structures (positive-positive, positive-invert, concave-convex) on the mechanical properties of cord-rubber composites through uniaxial tensile tests and finite element simulation. When the interlaced distance is 5 mm, the concave-convex overlap structure reaches the maximum tensile strength (74.79 MPa). With the increased interlaced distance, the failure form of the cord rubber composite gradually transfers from the overlap end to the interface slip and fixture end. The maximum Von Mises stress distribution of cord-rubber composite flexible support tends to be uniform through rational design by the mechanical characteristics of the three kinds of overlap structures.