Korteweg-de Vries (KdV)-type equation can be used to characterise the dynamic behaviours of the shallow water waves and interfacial waves in the two-layer fluid with gradually varying depth. In this article, by virtue of the bilinear forms, rational solutions and three kind shapes (soliton-like, kink and bell, anti-bell, and bell shapes) for the Nth-order soliton-like solutions of a coupled KdV system are derived. Propagation and interaction of the solitons are analyzed: (1) Potential u shows three kind of shapes (soliton-like, kink, and anti-bell shapes); Potential v exhibits two type of shapes (soliton-like and bell shapes); (2) Interaction of the potentials u and v both display the fusion phenomena.