Finding a physical approach for increasing the superconducting transition temperature (Tc) is a challenge in the field of material science. Shear strain effects on the superconductivity of rhenium were investigated using magnetic measurements, X-ray diffraction, transmission electron microscopy, and first-principles calculations. A large shear strain reduces the grain size and simultaneously expands the unit cells, resulting in an increase in Tc. Here we show that this shear strain approach is a new method for enhancing Tc and differs from that using hydrostatic strain. The enhancement of Tc is explained by an increase in net electron-electron coupling rather than a change in the density of states near the Fermi level. The shear strain effect in rhenium could be a successful example of manipulating Bardeen-Cooper-Schrieffer-type Cooper pairing, in which the unit cell volumes are indeed a key parameter.