This paper presents a theoretical investigation of nonlinear surface-wave propagation over a sloping bottom. For a problem with nonlinear surface-wave propagation over a sloping bottom, a perturbation method is first used to find the analytical solution in order to derive the third order terms for the bottom slope α and the wave steepness ε in the Eulerian system. Then, by transforming the flow field solution from the Eulerian system into the Lagrangian system, a more accurate wave profile is identified. By using the kinematic stability parameter, new theoretical breaking-wave characteristics are derived. The theoretical solutions are then compared with those from other research. The results reveal that the present solution reasonably describes the wave-breaking phenomenon. In this paper, a new theoretical solution for the breaking-wave characteristics is provided, and it is a useful approach for predicting breaking-wave characteristics.