The eigenvalue and the two-particle scattering matrix are obtained in a spin-ladder model. They are solved with the coordinate Bethe Ansatz method in integrable. The eigenvalue equation is formed with the Schrödinger equation. Then the eigenvalue is solved as the wave function is given. Finally, the two-particle scattering matrix is calculated by the eigenvalue equation and the continuous condition of the wave function. The eigenvalues of one-particle, two-particle and N₀-particle are solved, and the two-particle scattering matrix is obtained.