This paper shows the viscoelastic and nonlinear liver model for organ model based needle insertion, in which the deformation of an organ is estimated and predicted, and the needle trajectory is decided with organ deformation taken into consideration. An organ model including detailed material characteristics is important in order to achieve the proposed method. Firstly, the material properties of the liver are modeled from the measured data and its viscoelastic characteristics are represented by differential equations, including the term of the fractional derivative. Nonlinearity in terms of the stiffness was measured, and modeled using the quadratic function of strain. Next, a solution of an FE(Finite element) model using such material properties is shown. We use the sampling time scaling property as the solution for the viscoelastic system, while the solution for a nonlinear system using the Euler method and the Modified Newton-Raphson method is also shown. Finally, the deformation of liver model is calculated and pig liver of in vivo situation is obtained from medical ultrasound equipment. Comparing the relationship between needle displacement and force on real liver and liver model, we validate the proposed model.