The research is mainly made on the G1/C1 matching condition of spline curves. On the basis of the analysis on the basic function of T-B spline curves and the features of curve endpoints, we proposed the n+1 order T-B spline basic function and the solving method. The G1/C1 matching condition of C-B spline curves and T-B spline curves is put forward in this paper. On this condition, when matching C-B spline curves and T-B spline curves, the controlling vertexes can be added to make C-B spline curve tangent with the first and last edge by the first and last vertex of controlling polygon. Application instances were put up in this paper which illustrated that the G1/C1 matching between T-B spline curve and C-B spline curve using the feature of T-B spline curve which can represents semiellipse arc (semicircle arc) precisely can solve the problem that C-B spline curve cannot represents semiellipse arc (semicircle arc) precisely.