This paper describes a new method of position control of a pneumatic cylinder of which motions are simply repeated. A concept of time-optimal control and learning is introduced in the control method to realize high speed and a good transient response. The pneumatic system is basically composed of a pneumatic cylinder with a brake, a three-position solenoid-operated valve, a relay, a position sensor and a personal computer. Switching time of the valve is updated by learning after every repeated motion of the cylinder so that the piston rod has zero velocity at a desired position. Newton-Raphson's method and/or fuzzy reasoning are used as the learning methods. Experiments show that the learning is effective to make the cylinder motions converge to the desired steady ones and that the positioning accuracy of about 0.3 mm can be attained at the average velocity of the piston rod below about 1 m/s.