Abstract: For existing water conveyance systems, especially underground pipelines, the locations of sensors are typically difficult to adjust, which inevitably results in spatial blind zones during flow field monitoring. However, transient flow computations in viscoelastic pipelines usually rely on historical pressure information at specific locations, so conventional methods inherently lack the ability for spatial extrapolation. To address this issue, this study derives two extrapolation formulas for transient flow in viscoelastic pipelines based on the generalized Kelvin–Voigt viscoelastic constitutive model and the CTSS numerical scheme, and proposes an elastic–viscoelastic hybrid prediction–correction reconstruction algorithm (EPVC). Depending on the associated solution formulas, this study categorizes the full computational procedure into the E–V method and the V method. Numerical simulations and physical experiments show that the E–V method can achieve high-accuracy extrapolated reconstruction of transient flow fields: approximately 70% of the test cases have a root mean square error (RMSE) below 2.0, the maximum RMSE across all cases does not exceed 4.22, and the mean RMSE is only 1.46—representing a 46.02% reduction compared with the V method, thereby significantly improving reconstruction accuracy. Furthermore, this study employs Pearson correlation analysis, grouped trend analysis, and random forest feature contribution analysis to cross-validate the key operating parameters affecting reconstruction accuracy, and, based on this, defines the high-accuracy applicability range of the proposed method according to the probability distribution of high-precision operating conditions.