In this letter, an alternating-direction reduced finite-difference time-domain (ADI-R-FDTD) method is presents. 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 alternating-direction finite-difference time-domain (ADI-FDTD) method in 3 dimensions case, and the expression of the divergence relationship is derived. Based on the non-zero divergence relationship, the ADI-FDTD method is combined with the reduced finite-difference time-domain (R-FDTD) method. In the proposed method, the memory requirement of ADI-R-FDTD is reduced by1/12 of the memory requirement of ADI-FDTD averagely in 3D case. The formulation is presented and the accuracy and efficiency of the proposed method is verified by comparing the results with the conventional results.