Conventional Rashba spin polarization is caused by the combination of strong spin-orbit interaction (SOI) and spatial inversion asymmetry. However, Rashba- and Dresselhaus-type spin-split states are predicted in LaOBiS2 system by recent theory even though the crystal structure is centrosymmetric, which stem from the local inversion asymmetry of active BiS2 layer. By performing high-resolution spin- and angle-resolved photoemission spectroscopy, we have investigated the electronic band structure and spin texture of superconductor LaO0.55F0.45BiS2. Our studies present direct spectroscopic evidence for the local spin polarization in the vicinity of X point of both valence band and conduction band. Especially the coexistence of Rashba-like and Dresselhaus-like spin textures has been observed in the conduction band for the first time. The finding is of key importance for fabrication of proposed dual-gated spin-field effect transistor (SFET). Moreover, the spin-split band leads to a spin-momentum locking Fermi surface from which novel superconductivity emerges. Our demonstration not only expands the scope of spintronic materials but also enhances the understanding of SOI related superconductivity.