Shape-memory alloys (SMAs) are the metals which have the shape-memory effect. An alloy has peculiar temperature Tp, and the shape memory effect is observed when the body temperature is cooled to below Tp. The effect has been widely applied in different fields such as robotic muscles, medical surgeries, actuators and elastic wires. The SMA also has a unique characteristic to shrink at a certain temperature. The authors found a novel and interesting effect that, by making the SMA into a fine wire, it accepts a pulse-signal to generate a vibration in accordance with the pulse frequency of the signal, and have developed a vibration actuator for presenting tactile stimuli. By coupling the devices as a pair, a tactile display was constructed for presenting the phantom sensation and the apparent movement of the tactility, to transmit quite novel tactile sensations to a user. The information transmission by the device was tested by subjects, and was evaluated by questionnaires. The apparent movement was especially well perceived by users as a sensation of something running across fingers and a palm, or as being tapped by something, according to the well-determined signals given to the display. Several users reported that they perceived a novel rubbing sensation given by the apparent movement, and we further experimented the presentation of the sensation in detail to be used as a tactile display for the information transmission.