The ball aluminium oxide is produced with alpha-gibbsite powder, which is first produced into x-Al2O3 through fast dewatering at 400-800 deg.C for 0.05-0.5 sec, rolling to form ball, curing, hydration, drying and roasting at 450-500 deg.C. The x-Al2O3 is further produced into the ball aluminium oxide through treatment of water or ammonia water under saturated vapor pressure and at 120-220 deg.C, drying, soaking in the solution of lithium compound, drying and roasting at 600-700 deg.C. The ball aluminium oxide may be also produced by soaking x-Al2O3 directly in lithium compound solution and roasting after drying at 600-970 deg.C in the air. It has the features of large pores, low specific surface area and low acidity, and is suitable for use as carrier of catalyst for selective hydrogenation or hydramination of fatty alcohol.