The present invention provides a production method of a magnesium alloy material having excellent tensile strength and favorable ductility. Therefore, the magnesium alloy sheet material formed by rolling a magnesium alloy having a long period stacking order phase crystallized at the time of casting includes in a case where a sheet-thickness traverse section of an alloy structure is observed at a substantially right angle to the longitudinal direction by a scanning electron microscope, a structure mainly composed of the long period stacking order phase, in which at least two or more +-Mg phases having thickness in the observed section of 0.5 (mu)m or less are laminated in a layered manner with the sheet-shape long period stacking order phase.