A synthesis theory of ultra-wideband (UWB) bandpass (BP) transformer with short-circuited stubs is proposed in this paper. Based on the short-circuited stub number and their positions, six combination topologies are presented when the transmission line (TL) section is fixed to 4. Although analyzing the characteristic functions of these six combination topologies, the same theoretical Chebyshev transfer function can be summarized. Therefore, by selecting different short-circuited stub number and their positions, we can make a flexible choice of the filtering transformer pattern and keep the Chebyshev response at the same time. Finally, by using the proposed transformer, a UWB BP type Wilkinson power divider can be easily designed. In order to match the numbers and frequencies of output ports reflection zeroes (S-22 = 0)/isolation zeroes (S-32 = 0) with those of input port reflection zeroes (S-11 = 0), one extra TL and one isolation resistor are newly added in the power divider design. One experimental circuit is fabricated, and its measured frequency response verified well the proposed design theory and method.