In a worm-rack type transmission device (1) a curved side portion (6) is provided on rack teeth (2a) of a linear rack (2) in a manner to form a part of an ellipsoidal surface (E) and twisted by a changing rate (θ) of a torsional manner a toothed streak (5) of a worm wheel (3). The worm wheel (3) brings the toothed streak (5) into engagement with the curved side portion (6) in a line-to-line contact, enabling to a self-locking property and strengthening a transmission power to insure a high transmission efficiency with a least friction loss so as effectuate a linear drive for an extended distance travel with a high precision.