We investigated the magnetotransport properties of Fe-doped topological insulator Sb1.96Fe0.04Te3 single crystals. With doping, the band structure changes significantly and multiple Fermi pockets become evident in the Shubnikov-de Haas oscillations, in contrast to the single frequency detected for pure Sb2Te3. Using complementary density functional theory calculations, we identify an additional bulk hole pocket introduced at the Γ point which originates from the chemical distortion associated with the Fe dopant. Experimentally, both doped and undoped samples are hole-carrier dominated; however, Fe doping also reduces the carrier density and mobility. The angle dependent quantum oscillations of Sb1.96Fe0.04Te3 were analyzed to characterize the complex Fermi surface and isolate the dimensionality of each SdH feature. Among those components, we found two oscillations frequencies, which related to two Fermi pockets are highly angle dependent. Moreover, the fermiology changes via Fe doping and may also provide a different Berry phase, as demonstrated by the Landau fan diagram, thus indicating a rich complexity in the underlying electronic structure.