In this paper, linear accelerated turbulent pipe flow has been simulated at various Reynolds numbers using five common TURBULENCE MODELS. The MODELS considered are the Baldwin-Lomax algebraic model, the Spalart-Allmaras one-equation model, theκ-e model with wall correction of Lam and Bremhorst, theκ-ω model and the κ-ε-ν2 model. The goal is to evaluate the performance and precision of these MODELS for prediction of the wall shear stress, Reynolds stress, TURBULENCE viscosity, delay time in response and mean velocity. Factors such as changes in pipe diameter, fluid type, initial Reynolds number of acceleration and rate of acceleration and its effect on the above parameters has examined carefully. In order to verify the results, the experimental and numerical results (TURBULENCE modeling and Large Eddy Simulation) of other researchers have been compared with the present results. The results show the desired accuracy of the one-dimensional modeling of accelerated turbulent pipe flow in comparison with Large Eddy Simulation results (three-dimensional). The response of delay time, simulated by the MODELS (except BL model) shows relatively good agreement with experimental data. Comparing the distribution of mean velocity, turbulent kinetic energy and turbulent viscosity shows k-e-ν2 model leads to a better accuracy compared with the other MODELS.