In this paper, an optically transparency ultrawideband absorber with high angular stability is designed. The proposed absorber is composed of two different materials with indium thin oxide (ITO) conductive films and polydimethylsiloxane (PDMS) substrates. With the aid of a stacked structure design, the absorber has a 90% absorption band from 5 to 43.5 GHz and the fractional bandwidth reaches 158.7%. Also, for the TE mode, the absorption remains stable with the oblique incident angles reaching 50°. And similar angular stability can be observed for the TM mode from 0° to 70°. Besides, the thickness of the absorber is only 0.092 wavelength and transmittance within the visible band is 57.3%. For further verification, a prototype is fabricated and measured. Good agreements between the simulated and the measured results can be observed.