In a nonlinear optomechanical system which contains a Kerr medium and a degenerate optical parametric amplifier (OPA), optical bistability and entanglement are affected largely by these two kinds of medium. When adjusting the coupling constant of nonlinear crystal and the cavity field, the nonlinear gain of OPA crystal and the intensity of incident light have similar effects on the optical bistability, while the third-order nonlinear susceptibility of Kerr medium has obviously different effects. The calculation results of entanglement in this system show that the nonlinear gain coefficient of OPA crystal can increase the entanglement between cavity field and vibrating mirror, while the third-order nonlinear susceptibility of Kerr medium can reduce the entanglement.