Polymer flooding is one of the most incipient chemical-based enhanced oil recovery process that utilizes the injection of polymer solutions into oil reservoirs. The presence of a polymer in water increases the viscosity of the injected fluid, which upon injection reduces the water-to-oil mobility ratio and the permeability of the porous media, thereby improving oil recovery. The objective of this work is to investigate strategies that would help increase oil recovery. For that purpose, we have studied the effect of injection pressure and increasing polymer concentration on flooding performance. This work emphasizes on the development of a detailed mathematical model describing fluid saturations, pressure, and polymer concentration during the injection experiments and predicts oil recovery. The mathematical model developed for simulations is a black oil model consisting of a two-phase flow (aqueous and oleic) of polymeric solutions in one-dimensional porous media as a function of time and -coordinate. The mathematical model consisting of heterogeneous, nonlinear, and simultaneous partial differential equations efficiently describes the physical process and consists of various parameters and variables that are involved in our lab-scale process to quantify and analyze them. A dimensionless numerical solution is achieved using the finite difference method. We implement the second-order high-accuracy central and backward finite-divided-difference formula along the -direction that results in the discretization of the partial differential equations into ordinary differential equations with time as an independent variable. The input parameters such as porosity, permeability, saturation, and pore volume obtained from experimental data by polymer flooding are used in the simulation of the developed mathematical model. The model-predicted and commercial reservoir (CMG)-simulated oil production is in good agreement with experimental oil recoveries with a root-mean-square error (RMSE) in the range of 1.5-2.5 at a maximum constant pressure of 3.44 MPa as well as with temporal variation of the injection pressure between 2.41 and 3.44 MPa.