The procedure of attaining a compact bandpass filter (BPF) with dual band-notch function for ultra-wideband (UWB) applications is presented and discussed in this paper. In the proposed BPF defected ground structure (DGS) is used in order to improve the out-of-band performance of the filter and also four short-circuited bent stubs are employed in order to improve the selectivity of the filter at its cut-off frequencies. Dual band-notch function is added to the performance of the filter by coupling two short-circuited inverted T-shaped stubs to the filter main resonator. The fabricated filter satisfies well the demands of the Federal Communications Committee (FCC) with two narrow band-notch functions at 5.5 GHz and 8 GHz which eliminates the interference of the UWB system with WLAN and satellite communication systems, respectively. The improved upper stop-band of the proposed filter with more than 20dB attenuation level extends up to 20 GHz.