Elastic and damping properties of AZ31 magnesium alloy sheet processed by high-temperature rolling were investigated. The specimen rolled at high temperature (798 K) exhibited the significant low basal texture intensity and the wide spread of the basal pole toward the RD and TD, compared with the specimen rolled at 573 K. Young’s modulus of the specimen rolled at 798 K had smaller value at all angles than that of the specimen rolled at 573 K. Besides, the specimen rolled at 798 K exhibited slightly higher internal friction compared with the specimen rolled at 573 K over the strain amplitude range investigated. The suppression of the strong basal texture formation in the specimen rolled at 798 K likely contributed to a reduction of Young’s modulus and an increase in internal friction, because the breakaway stress, which is closely related to the macro-yield stress, decreases with an increase in the Schmid’s factor of basal slip.