In this work, we demonstrate that the near-field radiative heat transfer (NFRHT) between two graphene sheets can be modulated effectively, when the suspended sheets are subjected to mechanical strain. In this system, the isotropic optical properties of graphene dramatically change to be the in-plane anisotropy due to existence of the strain. The results suggest that the enhancement of NFRHT arises from the coupling of quasi-elliptic surface waves across the interfaces. We find that, by tuning the strain modulus or the stretching direction, the spectra of the heat transfer coefficient and the contour of energy transmission coefficient in k space are changed remarkably. These results indicate that the NFRHT is tunable. In a system whose strain is fixed at 23% and separation is 50 nm, a large change of NFRHT about 60% is achieved by tuning the stretching direction monotonously. Furthermore, we investigate the strain-induced modulation of the NFRHT under the different separations and carrier mobilities. This work provides a method to manipulate thermal radiation in a well controllable mode, and may have a potential impact on the development of micro/nano thermal management devices and systems.