In this paper, we will derive the two-dimensional extended Green-Naghdi system {see Matsuno [Proc. R. Soc. A 472, 20160127 (2016)] for determination in a various way} for flat bottoms of order three with respect to the shallowness parameter µ. Then we consider the 1D extended Green-Naghdi equations taking into account the effect of 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 new extended 1D system for a finite large time existence t = O(1 ε) is demonstrated.