The shear band is the critical component of a nonpneumatic tire (NPT) when determining the rolling resistance resulting from the elastomer's shear friction. In an effort to reduce the rolling resistance of an NPT, a shear band made of a porous, fiber-reinforced elastomer is explored. The porous shear band is designed to have the same effective shear modulus as the shear modulus of a continuous shear band. The originality of the study in this article is in the design of a flexible, porous solid for fuel efficiency of a tire structure by including a low viscoelastic energy loss material—a carbon fiber that partially replaces the volume of high viscoelastic energy loss material—polyurethane. To make the NPT structure remain flexible, porous volumes were included. Finite element (FE)–based numerical experiments with ABAQUS were conducted to quantify the reduced energy loss of an NPT using hyperelastic and viscoelastic material models. Load carrying capacity of the NPT with the designed porous shear band is also discussed.