A new polyisobutylene-based thermoplastic elastomer, poly(alloocimene-b-isobutylene-ballooci-mene triblock copolymer was synthesized by carbocationic polymerization, then electrospun intofree-standing rubbery fiber mats by adding 20 wt%. poly(ethylene glycol) to the solution. AlthoughAIBA is a highly hydrophobic material that is non-polar and therefore has high electric resistivity,fiber mats were still successfully obtained. We found that poly(ethylene glycol) was fully embeddedinto the electrospun fibers. The tensile strength measured on microdumbbells was 2.7 MPa at 537%elongation that is comparable to that of soft human tissues. These rubbery fiber mats were foundto be hydrophobic and cell culture studies showed their non-cytotoxicity. Based on these favorableproperties, these fiber mats show a great promise for tissue scaffold and drug delivery applications.