Although possible non-homogeneous strain effects in semiconductors have been investigated for over a half century and the strain-gradient can be over 1% per micrometer in flexible nanostructures, we still lack an understanding of their influence on energy bands. Here we conduct a systematic cathodoluminescence spectroscopy study of the strain-gradient induced exciton energy shift in elastically curved CdS nanowires at low temperature, and find that the red-shift of the exciton energy in the curved nanowires is proportional to the strain-gradient, an index of lattice distortion. Density functional calculations show the same trend of band gap reduction in curved nanostructures and reveal the underlying mechanism. The significant linear straingradient effect on the band gap of semiconductors should shed new light on ways to tune optical-electronic properties in nanoelectronics.