Recent cosmic-ray measurements by the ATIC, CREAM and PAMELA experiments have found an apparent hardening of the energy spectrum at TeV energies. Although the origin of the hardening is not clearly understood, possible explanations include hardening in the cosmic-ray source spectrum, changes in the cosmic-ray propagation properties in the Galaxy and the effect of nearby sources. In this contribution, we propose that the spectral anomaly might be an effect of re-acceleration of cosmic rays by weak shocks in the Galaxy. After acceleration by strong supernova remnant shock waves, cosmic rays undergo diffusive propagation through the Galaxy. During the propagation, cosmic rays may again encounter expanding supernova remnant shock waves, and get re-accelerated. As the probability of encountering old supernova remnants is expected to be larger than the young ones due to their bigger size, re-acceleration is expected to be produced mainly by weaker shocks. Since weaker shocks generate a softer particle spectrum, the resulting re-accelerated component will have a spectrum steeper than the initial cosmic-ray source spectrum produced by strong shocks. For a reasonable set of model parameters, it is shown that such re-accelerated component can dominate the GeV energy region while the non-reaccelerated component dominates at higher energies, explaining the observed GeV-TeV spectral anomaly.