PURPOSE: To permit a braking power to be gradually enlarged and achieve a multi-stepped braking operation, by forming a solenoid for operating a brake booster in such a manner that a movable iron core is gently attracted upon energizing the solenoid, and it is rapidly returned upon deenergizing the solenoid.

CONSTITUTION: When a coil 2 of a solenoid A is energized, a movable iron core 3 is rightwardly attracted, wherein the iron core 3 is slowly attracted because pressure in a buffering chamber 10 is increased owing to a small aperture 5a of a valve 5. Accordingly, a rod 24 of a valve piston 23 of the brake booster is slowly attracted to gradually operate the brake booster. When the coil 2 is deenergized, the movable iron core 3 is returned, wherein the valve 5 is opend, and air is freely induced into the buffering chamber 10, thereby permitting the iron core 3 to be rapidly returned. As a result, the brake booster is rapidly returned.