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In this study, both a new damper concept and its mathematical model are proposed. Basically, a damping force for an oil damper depends on a stroke speed. Therefore, a damper becomes stiff in a high speed stroke if a higher damping coefficient was set up to improve a dynamic performance. As a result, a ride comfort for a vehicle would be spoiled. A relationship between a dynamic performance and a ride comfort are trade-off. It is necessary to consider desirable damping force characteristics. However, it is a complicated issue to treat oil dampers theoretically. The study aims to develop a new nonlinear damper and its mathematical model. The damper has two main features: an ease to design a characteristics of damping force and a damping force reduction mechanism. The damping force generation mechanism of the damper is based on a viscous theory. A mathematical model of the damper is also developed using simple formulations. The simulated result of a damping force vs stroke speed using the mathematical model shows a damping force decrease in high piston speed. In addition, the prototype of the damper was developed and tested for the validation of the mathematical model. The simulated damping force characteristics agreed well with the actual one.