This paper considers a positioning problem of high-speed trains (HST) in railway wireless network by utilizing the 5G new radio (NR) positioning reference signals (PRS). It is assumed that the train runs along the railroad at a fixed velocity and receives PRS signals from the base stations (BSs) deployed on the side of the railroad. To deal with the positioning problem, an iterative two-phase weighted least squares (I2WLS) method based on range difference of arrival (RDOA) measurements is proposed, which linearizes the RDOA equations to pseudo-linear ones. The accuracy gap between RMSE of the proposed approach and Cramer-Rao lower bound (CRLB) is small when the RDOA measurements noise level is sufficiently small. Furthermore, the simulation results illustrate that a high, centimeter-level accuracy can be achieved for small PRS intervals, velocities and base station distances.