A connector to join the backrest frames and the handle grip of a stroller includes a first and a second tubular member, a toothed wheel, a coil spring, a circular plate and a fastening device. The toothed wheel has a pair of shallow grooves and a pair of tapered grooves formed within its inner wall. The first tubular member has first annularly spaced teeth formed in its inner wall, which are adapted to accomodate the toothed wheel. The diameter of one end of the tubular member is smaller that that of the other end. The second tubular member has a closed end with a through hole and an open end. Second annularly spaced teeth are formed within its inner wall, which are aligned with the first annular teeth, so that the toothed wheel can slide axially within the confines of the first and the second tubular member when they are engaged. The circular plate has a pair of engaging members adapted to engage the pairs of grooves.