This paper introduces an approach to the optimum design of ultra-wideband (UWB) bandpass filter based on step-impedance resonator (SIR's). We consider a SIR resonator with parallel-coupled I/O line, where the filtering function can be easily derived based on conventional even-odd mode technique. It was shown that the number of transmission poles depends on the length of low impedance section. The filtering function F(�) possesses a frequency-dependent sine term in the denominator yielding a non-Chebyshev response. In order to exhibit an optimum response in terms of selectivity from passband to stopband, technique of quasi-Chebyshev function approximation to achieve equiripple in the passband was synthesized. The present work shows a simple and direct method that allows for a computation of characteristic impedances to produce the equal-ripple bandpass filter with desired bandwidth and ripple level. A prototype of 5 GHz has been fabricated to validate proposed synthesis. © 2014 Taylor & Francis.