A self-opening/closing umbrella includes a central shaft unit having an improved structure. The central shaft unit forms a raised channel on one side of a third shaft segment and a pulley is pivotally mounted to a lower portion of the raised channel. A second shaft segment has a top to which an internal plug including a pulley is fixed and includes a first pull rope having an end fixed to a bullet-head member and an opposite end extending upward to warp around the pulley of the internal plug, projecting through a sideway slot, extending downward to wrap around the pulley inside the third shaft segment for upward extension to fix to a top end of the third shaft segment. A second pull rope has an end fixed to the internal plug and an opposite end extending across a top cap to project outward to fix to the runner.