A fairing transition curve is constructed between two nonadjacent cubic TBézier curves based on C2 continuity. Firstly, the adjacent endpoints of two curves are considered as the target points, and then according to the C2 continuous extension method of cubic TBézier curve, two auxiliary extension curves are produced, respectively. Secondly, a blending extension curve with a balance factor are constructed based on a class of rational trigonometric blending functions and two auxiliary extension curves. Lastly, regarding the formal approximation of blending extension curves strain energy as objective function, a fairing blending extension curve is determined by minimizing the object function. Moreover, this method is also applied to the extension of cubic TBézier surface in this paper. Experimental examples show that the extension curves and surfaces have better fairness.