Abstract: In this paper, it is proven that the divergence relationship of electric-field and magnetic-field is non-zero even in charge-free regions when the electric-field and magnetic-field are calculated with locally one-dimensional finite-difference time-domain(LOD-FDTD)method,and the concrete expression of the divergence relationship is derived.Based on the non-zero divergence relationship and Maxwell curl equations set,the LOD-FDTD method which is unconditionally stable is combined with the reduced finite-difference time-domain(R-FDTD)method.In the LOD-R-FDTD method, the advantage of LOD-FDTD is combined,which having simpler formulation to eliminate the restraint of the courant-friedrich-levy(CFL)condition.The memory requirement of LOD-R-FDTD is reduced by 1/3 compared with LOD-FDTD in average.The formulation is presented and the accuracy and efficiency of the proposed method is verified by comparing the results with the conventional results.