Abstract: Finite volume method with second-order Godunov-type scheme was developed to simulate the water column separation and rejoining phenomenon in viscoelastic water pipes. Based on the traditional elastic pipe model, the viscoelastic effect was considered in the process of numerical simulation. The viscoelasticity term and unsteady friction term were introduced into the governing equation of hydraulic transient flow, and the finite volume method with second-order Godunov scheme was used to solve the problem of numerical discretization and calculation. The pressure adjustment coefficient was considered to calculate the influence of free gas on the calculation unit, meanwhile the slope limiter MINMOD function was introduced for the sake of avoiding the spurious oscillations of numerical simulation results. The ghost cell method was used to construct the boundary and realize the unified computation of computing area at the same time. The calculation results of the model established in this paper were compared with those of the existing model and the experimental results, and the sensitivity analysis of the influencing parameters was also carried out. The results show that the proposed model can accurately simulate the transient pressures fluctuation and changes in the cases of both pure water hammer and water column separation and rejoining water hammer, which were basically identical with the experimental data. Compared with the traditional MOC method, when the Courant number C_r is less than 1, the results of finite volume method's second-order Godunov scheme are more accurate and stable. In the process of pressure attenuation, viscoelastic effect plays a dominant role compared with pipeline friction. Compared with the mathematical model which only considers the elasticity of the pipe, the accuracy of simulation results can be significantly improved by considering the viscoelastic effect of the pipe, especially the relative error of the peak value of the pressure wave is significantly reduced.