We studied a possible mechanism for the highly sensitive response of electrical resistivity to strain in metal Cr by means of theoretical calculation and experimental measurement. First-principles calculations based on density functional theory were performed for antiferromagnetic Cr in the spin-density wave (SDW) state. The calculation succeeded to reproduce a significant magnetovolume effect by hydrostatic pressure observed in Cr, and the obtained result revealed that the electronic structure and magnetic properties in the SDW state are sensitive to uniaxial strain. The magnetic moment of Cr changed more than 5% with a strain of 1%. We estimated the gauge factor (GF), which denotes the sensitivity of resistance to strain, from the local density of states. The obtained GF value of Cr in the SDW state was found to be approximately 10, whereas that of Cr in the nonmagnetic state, Fe in the ferromagnetic state, and V in the nonmagnetic state was around 1. This result was consistent with our experimental measurement of the GF of Cr, Fe, and V thin films. We found that the large GF is related to a significant magnetovolume effect in Cr. The volume variation accompanying uniaxial strain influences both the magnetic state and electrical conduction of Cr through sensitive changes of the electronic structure in the SDW state.