A new type of eccentric cylindrical gear rack mechanism is introduced. The gear is normal cylindrical gear which is eccentrically installed and the pitch curve of the rack is plane curve. The gear and rack are engaged with each other so that a special request of movements can be achieved. According to the fundamental law of mating profile,the equations of the pitch curve of the rack can be deduced. And further,the tooth profile equations of the rack are calculated based on the concept of the counterpart rack. Eventually,the3-dimentional modeling and motion simulation of the mechanism are carried out,through which the correctness of the design and modeling is preliminarily confirmed.