Abstract: The new-old concrete composite beams are considered as an important engineering beam with a bond-slip in the composite surface. Based on the deformation compatibility relationship across the composite surface of the new-old concrete composite beam, a nonlinear differential equation is derived, for the axial force of the new-old concrete composite beam. The theoretical expressions of the section coordination coefficient are obtained from the equation. With the coordination coefficient, a practical nonlinear analysis method is established, which can exactly describe the shrinkage and the creep of the new-old concrete composite beams. The Bernoulli assumption and the coordination coefficient of the section are duly combined. Compared with the existing analytical solutions, the accuracy can meet the engineering requirements.