In this paper, a new algebraic closure model for the DNS of turbulent drag reduction in a channel flow using microfiber additives is presented. This model is an extension of an existing model and cures some the shortcomings of the old model. In the proposed model, using the velocity correlation tensor in the modeling process, more physical conditions of the flow field are taken into account. With this, some of the shortcomings of other models are cured. The proposed model is used to directly simulate turbulent drag reduction in a horizontal channel flow under the action of a constant pressure gradient. For this purpose, time-dependent, three-dimensional Navier-Stokes equations for the incompressible flow of a non-Newtonian fluid are numerically solved. Statistical quantities of obtained by the new model are compared with the results of previous simulations. The good agreement between the results demonstrates the proper accuracy of the new model. Especially, the root-mean-square of velocity fluctuations in the streamwise direction is predicted with high accuracy as compared to previous models. Other statistical quantities are also computed with appropriate accuracy. This model is capable of prediction all properties of a microfiber-induced drag-reduced flow.