In this article, we study the near-field radiative heat transfer (NFRHT) between two graphene sheets under mechanical strain. The modulation of NFRHT due to the strain modulus and stretching direction is investigated under two types of strain configurations. For the first type, one graphene sheet is strained whereas the other one is unstrained. It is found that the spectra of NFRHT undergo a redshift and the magnitudes drop remarkably as the strain modulus increases. For the second type of configuration, two graphene sheets have the same strain modulus while the stretching direction could be arbitrary. It is found that the differences in stretching directions lead to the mismatch of anisotropic plasmonic modes. Under proper choices of stretching directions, a large modulation with the reduction of heat transfer coefficient over 60% is possible for strain modulus 0.2. Our findings may have promising applications in thermal management for micro/nano-electromechanical devices.