In this paper, a miniaturized ultra-wideband( UWB) microstrip antenna with independent tunable double band-notched characteristics is presented, which consists of the semicircle ring-like radiating patch with an elliptical-shaped slot and double split ring resonators(SRRs) on the top surface of the substrate and defected ground structure(DGS) on the bottom surface of substrate. The operating frequencies have range from 1.3GHz to 11.6GHz(S11<-10dB). The double band-notched characteristics have been achieved by etching elliptical-shaped slot at the radiating patch and placing double C-shaped SRRs at the both side of the microstrip feed line. By loading varactor diodes at the gap of the elliptical-shaped slot and the double C-shaped SRRs and changing the reverse-bias control voltage of the varactor diodes, the notch frequency can be electronically tuned efficiently. The experimental results, which are agree well with the simulated results, demonstrate that the proposed antenna have created the notched frequency band shift from 2.47GHz to 4.19GHz(1.72GHz) and 4.32 GHz to 5.96GHz(1.64GHz) when the reverse bias voltage vary from 0V to -30V corresponding to the junction capacitance of varactor diode has decreased from 2.67pF to 0.63pF, which imply that the proposed antenna with band-notched characteristics has the capability to suppress the narrow interference signals which cover the wireless local area network(WLAN) and world interoperability for microwave access(WiMAX) band. Furthermore, the proposed antenna structure only has the electrical size of 0.26λ*0.19λ at 1.3GHz. Compare to the related reported antennas, the proposed antenna has achieved compact size, tunable dual band-notched characteristics and good band-notched performance simultaneously to the best of our knowledge. It is believed that the proposed antenna will have a very valuable prospect in the fields of wireless body area network (WBAN), UWB communication, Internet of Things(IoT), etc.