An algebraic closure for the non-Newtonian Navier-Stokes equations is presented which accounts for the effect of a dilute suspension of Brownian fibers. The model is intended to be used in simulations of turbulent drag reduction by Brownian fiber additives. It is based on a blending between an existing algebraic model for non-Brownian fibers and an analytical result for strongly Brownian fibers. Two-way coupled simulations of turbulent drag reduction in a channel flow demonstrate that the model predicts flow statistics that are in very good agreement with those obtained by the direct Monte-Carlo approach. Using the proposed model, the cost of simulating a drag-reduced flow in terms of CPU-time is slightly more than that of a Newtonian flow. (C) 2015 Elsevier B.V. All rights reserved.