Recently various kinds of tasks such as the inspections on the curved wall of a vessel are performed by mobile robots. In those cases, the robot has to travel on curved surfaces along the prespecified path and has to know its current position for the successful accomplishment of the tasks. In this paper, we propose a dead-reckoning formula for a two-wheeled mobile robot moving on a curved plane, and illustrate the formula with examples for cylindrical surfaces. The performance of the proposed algorithm will be analyzed through a series of experiments by the magnet wheeled mobile robot developed in our laboratory.