A height adjustable device is received in the inner tube which is retractably inserted in an outer tube, and includes a base which is fixed in the inner tube and two stop plates are pivotably connected of the base. Two respective first ends of the two stop plates extend through apertures defined through the inner tube and are in contact with two respective insides of the outer tube so as to position the inner tube. A member is movably connected to the base and includes a driving portion for pivoting two respective second ends of the two stop plates. A cable is connected between the movable member and a pivotable member fixed to the inner tube. The pivotable member is pivoted to pull the cable and the two stop plates are pivoted inward so that the inner tube can be freely moved in the outer tube.