The coupling of velocity dispersion curves of leaky Lamb waves is studied based on numerical calculations. The bilayers consisting of two thin plates with various thickness ratios can be regarded equivalently as single-layered plates with various material properties between those of the original two materials in terms of the leaky Lamb wave velocities. The phase velocity dispersion curves, the imaginary parts of the complex-valued velocity and the particle displacements corresponding to the fourth and fifth modes are discussed varying the thickness ratios of the two plates. An interesting phenomenon about the velocities of the two modes is found for several combinations of two parameters of the thickness ratio and the product of frequency and the total thickness of the bilayer. The phenomenon, which is called mode coupling in this article, is similar to the behavior of the mathematical function ω= z 1/2 on the complex plane. Mode repulsion and mode crossing of dispersion curves are described as two different types of mode coupling.