Polymer flooding is an enhanced oil recovery (EOR) method which improves the mobility ratio and sweep efficiency of a waterflood. In theory, the high viscosity of the polymer reduces its injectivity compared to water. However, field studies have documented much higher polymer injectivity than predicted by theoretical models. There are various reasons for high polymer injectivity. The objective of this work is to predict polymer injectivity in granular media accounting for fluid-induced fractures, water quality, polymer rheology, and undissolved polymers. We perform grain-scale, coupled fluid dynamics and granular mechanics modeling. Fluid-particle interactions are modeled by coupling computational fluid dynamics (CFD) and the discrete element method (DEM). Simulation results show that polymer injection can create fractures in the granular media along the direction perpendicular to the minimum principal stress, thereby reducing wellbore pressure buildup at a constant polymer injection rate. The polymer tends to flow in the direction of fracture propagation in granular media, so the direction of the fracture affects the swept area of the polymer. Polymer rheology, water quality, and undissolved polymer also affect the polymer injectivity. Suspended solid particles may plug pores and reduce the injectivity of polymer by ~25%. Mechanically trapped undissolved polymers can greatly reduce polymer injectivity in low-permeability granular media. This work shows for the first time initiation of polymer-driven fractures in a granular model and demonstrates its implications on polymer injectivity.