Reynolds-averaged modeling is performed for polymer-induced drag reduction (DR) fluid at the fully developed turbulent regime in a concentric annulus by using the commercial code, ansys-fluent. The numerical approach adopted in this study relies on a modified k–ε––f model to characterize the turbulence and the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model to represent the rheological behavior of the polymer solution. The near-wall axial velocity, Reynolds stress, and turbulent kinetic energy (TKE) budget near both walls of the annulus (fixed radius ratio of 0.4) are compared in detail at a constant Reynolds number () and various rheological parameters (Weissenberg number in the range of 1–7 and the maximum polymer elongation L = 30 and 100). Current simulation has predicted the redistributions of turbulent statistics in the annulus, where the two turbulent boundary layers (TBLs) of the DR flow differ more compared to those of its Newtonian counterpart. The difference is also found to be highly dependent on the rheological properties of the viscoelastic fluid.