This study was to investigate the effects of stress ratio and anisotropy on Fatigue Crack Propagation(FCP) behavior of rolled magnesium alloy AZ31B. The experimental materials were a Mg-Al-Zn magnesium alloy. The FCP test was conducted on compact tension specimen by a servo-hydraulic fatigue testing machine in air at room temperature. Compact tension specimens were prepared from the extruded parallel and vertical rolling direction. The test condition was frequency of 10Hz and sinusoidal load stress ratios are 0.1 and 0.7. The FCP rates was automatically measured by a compliance method. In the case of the FCP of AZ31B, the FCP of both direction of LT and TL by anisotropy of specimens are almost same value. In lower stress ratio, the FCP of the LT, TL specimens are increased in lower ${Delta}K$ region but higher ${Delta}K$ regions are almost same value. Finally, the result of observed the surface crack, it expressed the quasi-cleavage fracture in lower ${Delta}K$ region and straight mark on the aspect of the facet in high ${Delta}K$ region.