High perpendicular magnetic anisotropy (PMA), a property needed for nanoscale spintronic applications, is rare in oxide conductors. We report the observation of a PMA up to 0.23 MJ/m3 in modestly strained epitaxial NiCo2O4 (NCO) films which are room-temperature ferrimagnetic conductors. Spin-lattice coupling manifested as magnetoelastic effect was found as the origin of the PMA. The in-plane xx-yy states of Co on tetrahedral sites play crucial role in the magnetic anisotropy and spin-lattice coupling with an energy scale of 1 meV/f.u. The elucidation of the microscopic origin paves a way for engineering oxide conductors for PMA using metal/oxygen hybridizations.