Direct numerical simulation (DNS) of viscoelastic turbulent flow, due to its importance in predicting drag reduction and developing viscoelastic turbulent models has become as a considerable portion of non-Newtonian fluid flows studies. In the present work, after introducing the phenomenon of drag reduction, the unsteady 3-D governing equations of a duct flow required for DNS of viscoelastic turbulent flow using Giesekus model are employed. To obtain the numerical results, a new solver based on finite volume method is developed in Open FOAM software. Comparing turbulent characteristics of viscoelastic flow with Newtonian one, the drag reduction value is calculated. The obtained results are compared with the corresponding values from a similar study based on finite difference method using the same rheological parameters (Re?=150, We?=30, b=0.9 and a=0.001) and a good agreement is observed. The effect of varying the mobility factor ? and viscosity ratio ? on the drag reduction and flow characteristics is investigated.