exploded perspective view showing the first embodiment of the present invention and illustrates a case where the present invention is applied to a front seat of an automobile in the following description the same components as in the conventional example shown in fig9 and 10 will be denoted by the same reference symbols as used above a headrest 2 is supported by inserting headrest stays 3 a and 3 b into tubular headrest bushes 6 a and 6 b respectively the headrest stays 3 a and 3 b are attached to the headrest 2 to support it the headrest bushes 6 a and 6 b are securely installed on the side of a seat back 1 the two headrest stays 3 a and 3 b are laterally arranged as shown in fig5 the headrest bushes 6 a and 6 b are fixed to a seat back frame 11 of the seat back 1 more specifically the headrest bushes 6 a and 6 b are fixed by being inserted into tubular attachment members 14 which are firmly fixed to the seat back frame 11 while the headrest bush 6 a is provided with a height adjusting mechanism 7 the headrest bush 6 b is provided with a falloff preventing device 9 the height adjusting mechanism 7 can stop hold the headrest 2 the headrest stay 3 a at an arbitrary height the falloff preventing device 9 can prevent the headrest 2.