An efficient three-dimensional (3-D) fundamental locally one-dimensional finite-difference time-domain (FLOD-FDTD) method incorporated with memristor is presented. The FLOD-FDTD method achieves higher efficiency and simplicity with matrix-operator-free right-hand sides (RHS). The updating equations of memristor-incorporated FLOD-FDTD method are derived in detail. Numerical results are provided to show the trade-off between efficiency and accuracy.