The heat produced by the fission in the fuel of HANARO, 30 MW of research reactor, was transferred from the primary cooling water to the secondary cooling water through heat exchangers. The secondary cooling water absorbing the heat was circulated by secondary cooling pumps and cooled through 33 MW of cooling tower. Each capacity of the three secondary cooling pumps was fifty percent ($50\%$) of full load. The two pumps were normally operated and the other pump was standby. One of the secondary cooling pumps has often made troubles by high vibration. To release these troubles the pump shaft has been re-aligned, the pump bearing has been replaced with new one, the shaft sleeve has been replaced with new one, the shaft and the impeller have been re-balanced representatively and/or the vibration of motor has been tested by disconnecting the shaft of pump. But the high vibration of pump cannot be cleared. We find out the weight balance trouble of the assembly in which the impeller is installed in the shaft. After clearing the trouble, the high vibration is relieved and the pump is operated smoothly. In this paper, the trouble solution shooting method of secondary cooling pump is described including the reason of high vibration