We suggest that the production of Galactic cosmic rays in supernova remnants undergoes two stages of acceleration mechanisms. Cosmic rays are first accelerated to certain cut-off energy that is significantly below the knee energy by the shock front. They then are further accelerated stochastically by compressive plasma fluctuations in the downstream region to the knee energy. If the compressive plasma fluctuations appear as an ensemble of shocklets, the stochastic acceleration process raises the cut-off energy without changing the shock power-law spectrum. In this way, the nonlinear shock acceleration effects become less severe, and it is not necessary to amplify upstream interstellar magnetic field to mG in order to make cosmic rays reach the knee energy.