Thermocapillary migration of a liquid slug is caused by temperature difference between the ends of a slug. The temperature difference induces the difference of the surface tension coefficient and consequently of capillary pressure between the ends of the slug. Presently available model to predict a velocity of thermocapillary migration adopts the Poiseuille equation which is valid only for a very long slug and neglects the shear stress near the contact line. In the present study, a new model has been developed to consider the shear stress near the contact line so that it can be applied to slugs or drops of general configuration. The experiments using mineral oil with the length to diameter ratio being 10 and a glass capillary were performed. It was found that the liquid slug began to move upon overcoming contact angle hysteresis when the temperature difference reached 35$^{circ}C$. The results indicate that the new model well predicts the velocity of the liquid slug.