For understanding the deformation mechanism of AZ31 Mg alloy, two kinds of specimen, hot-rolled sheet and extruded bar were tested in tension at room temperature. Relatively small grain sizes ranging from 32 to 8.7 (m are obtained by annealing at several temperatures. And then they were further cold-rolled with rolling angles of 0-, 45- and 90-, which is the angle between the rolling and the longitude direction of as-received specimen, and annealed at a temperature in recrystallization field. The yield stress were found from the stress-strain curve. The grain size dependence of the yield stress is found not in agreement with the Hall-Petch relationship. The texture of (0002) pole figure of each kind of specimen was tested by X-ray diffractometer. The specimen with strong basal texture shows large yield stress and low work-hardening rate, while the specimen with weak basal texture shows low yield stress and rapid work-hardening rate. These results are interpreted by the slip system activated in the different textures. A combined slip system was used to interpret the yield stress variation with the texture and the deformation mechanism was discussed.