In this paper, a derivation of the two-dimensional asymptotic nonlinear highly dispersive shallow-water extended Green-Naghdi system for an uneven bottom is represented. Then we consider the one-dimensional case of this model taking into consideration the e ect of a small surface tension. We show that the construction of solution with a standard Picard iterative scheme can be accomplished in which the well-posedness in X s = H s+2 (R) ◊ H s+2 (R) for some s > 3 2 , of the modified extended one-dimensional system for a finite large time existence t = O(1 Á‚-) is proved.