Recent studies indicate that the texture distribution in friction stir welded (FSW) Mg alloys can be tailored and hence improve the joint performance. In this work, a crystal plasticity finite element modeling (CPFEM) was performed to understand the effects of texture distribution in stir zone (SZ) on the non-uniform plastic deformation and fracture localization. In total, six kinds of observed or purposely tilted texture distributions were modelled. The “concave-convex” appearance, as commonly observed in the tensile sample, was successfully simulated. It reveals that the mirror-symmetrical distribution of basal planes in the region of easy to activate basal slip (EABS) determined the “concave-convex” appearance in SZ-center. The asymmetrical appearance exchanged on plane A and plane B when the directions of basal planes were switched in the two EABS regions. Furthermore, the asymmetrical feature of plastic deformation was changed with varying the texture distribution in SZ. The “embossed” feature became more obvious in SZ-center first, and then gradually weakened with the c-axis rotated away from the weld plate plane. Severe necking was successfully simulated in SZ-center of FSW-H joint and in SZ-side of FSW-L joint. That might determine the observed fracture morphology. We believe that this simulation study is helpful for further improving the performance of FSW Mg joints.