A bypass valve apparatus may include an upper body, a lower body in which the upper surface thereof is coupled with the lower surface of the upper body and the lower surface thereof is coupled to an upper end portion of the compressed air passage, a solenoid disposed in the upper body, a plunger movable in the hollow of the upper body and the hollow of the lower body depending on the electric source supplied to the solenoid, a return spring returning the plunger to the original position when the electric source of the solenoid is released, an inlet, an outlet formed at a side end portion of the lower body, and a taper groove formed in a taper shape at a portion spaced from the outlet on an internal circumference in the hollow of the lower body.