A strand guiding apparatus includes a plurality of pairs of rollers arranged along a moving direction of a strand, a plurality of drive motors for generating driving forces to drive the pairs of rollers, a plurality of worm reducers for transmitting the driving forces of the drive motors to the pairs of rollers while reducing the rotational speed of the drive motors, each worm reducer having a worm extending in a direction orthogonal to an axis of the corresponding roller, and operable to transmit a load occurring at the roller to the corresponding drive motor, and a control unit for controlling the respective rotational speeds of the rollers and/or the respective driving forces of the drive motors based on the load to the drive motors. The reliable control for drive rollers can be attained to have a proper rotational speed without causing a reduction in surface quality and chatter in a strand guiding apparatus for continuous casting equipment using worm reducers.