The local electronic and atomic structures of the high-quality single crystal of SrFeO3-δ (δ~0.19) were studied using temperature-dependent x-ray absorption and valence-band photoemission spectroscopy (VB-PES) to investigate the origin of anisotropic resistivity in the ab-plane and along the c-axis close to the region of thermal hysteresis (near temperature for susceptibility maximum, Tm~78 K). All experiments herein were conducted during warming and cooling processes. The Fe L 3,2-edge X-ray linear dichroism results show that during cooling from room temperature to below the transition temperature, the unoccupied Fe 3d e g states remain in persistently out-of-plane 3d 3z2-r2 orbitals. In contrast, in the warming process below the transition temperature, they change from 3d 3z2-r2 to in-plane 3d x2-y2 orbitals. The nearest-neighbor (NN) Fe-O bond lengths also exhibit anisotropic behavior in the ab-plane and along the c-axis below Tm. The anisotropic NN Fe-O bond lengths and Debye-Waller factors stabilize the in-plane Fe 3d x2-y2 and out-of-plane 3d 3z2-r2 orbitals during warming and cooling, respectively. Additionally, a VB-PES study further confirms that a relative band gap opens at low temperature in both the ab-plane and along the c-axis, providing the clear evidence of the charge-density-wave nature of SrFeO3-δ (δ~0.19) single crystal.