Purpose <p>Impact-based vibration energy harvesters can increase power conversion efficiency by widening the operating frequency bandwidth and reducing resonant frequency. Viscoelastic material also can improve the energy harvesting performance. The stochastic dynamics of impact-hybrid energy harvesting with viscoelasticity has been less studied. This paper investigates the stochastic response of impact-hybrid energy harvesting with viscoelasticity in the presence of additive and multiplicative noise.</p> Methods <p>The proposed method is based on the stochastic average method and non-smooth transformation. Viscoelastic force is replaced by the damping and stiffness terms. The stationary probability density functions of the amplitude, velocity and displacement of impact-hybrid energy harvesting with viscoelasticity are derived by using non-smooth transformation and the stochastic averaging method. The validity of the method is verified by comparing the numerical simulation results with the analytical results. </p> Results <p>The validity of the proposed method is verified by comparing the numerical simulation results with the analytical results. Stochastic P-bifurcation phenomenon is analyzed based on the variation of the peak number of the joint probability density function</p> Conclusion <p>The linear damping coefficient and the restitution coefficient can induce the stochastic P-bifurcation phenomenon. Increasing the noise intensity can improve the output performance.</p>