Recent cosmic ray (CR) experiments discovered that the CR spectra experience a remarkable hardening for rigidity above several hundred GV. We propose that this is caused by the superposition of the CR energy spectra of many sources that have a dispersion in the injection spectral indices. Adopting similar parameters as those of supernova remnants derived from the Fermi γ-ray observations, we can reproduce the observational CR spectra of different species well. This may be interpreted as evidence to support the supernova remnant origin of CRs below the knee. We further propose that the same mechanism may explain the "ankle" of the ultra high energy CR spectrum.PACS numbers: 98.70. Sa,96.50.sb,98.38.Mz Introduction-Nearly 100 years after the discovery of cosmic rays by V. Hess in 1912, several basic questions on CRs, such as the source(s) and the propagation effects, are still not well understood. Precise measurements of the CR spectra and observations of high energy γ-rays and neutrinos, are of great importance to approach the answers to these fundamental questions.