The virtual training system of vascular interventional surgery can improve the operation level of novice interventional surgeons and reduce the training cost. The deformation simulation of vascular tissue is the key part of the virtual training system for vascular interventional surgery. This paper presents a vascular tissue model based on nonlinear viscoelastic tensor-mass method (NVTMM), which can realize real-time visual feedback and haptic feedback. The hyperelastic model is used to simulate the nonlinear viscoelastic behavior of blood vessels. Meanwhile, the Euler's implicit integration scheme is used to make the simulation results more stable. In addition, a haptic force feedback device is introduced for the interaction between the vascular model and the virtual medical instrument, which improves the authenticity of the simulation. Finally, the real-time performance and accuracy of NVTMM, MSM and FEM are compared through experiments. The results show that NVTMM method has high real-time performance and can reflect the nonlinear viscoelastic behavior of blood vessels to a certain extent.