As an allotrope of graphene, T-graphene was predicted to be an intrinsic two-dimensional (2D) superconductor with a superconducting critical temperature (Tc) of about 20.8 K [Gu et al., Chin. Phys. Lett. 36, 097401 (2019)]. In this work, based on first-principles calculations, hole doping and biaxial tensile strain (BTS) are considered to modulate the electron-phonon coupling (EPC) and superconductivity of T-graphene. It is found that the EPC constant of T-graphene is 0.807 and the calculated critical temperature Tc is 28.2 K at a doping level of 0.5 hole per unit cell (3.31 × 1014 cm-2) and 12% BTS. Furthermore, when 0.8 hole per unit cell (5.43 × 1014 cm-2) doping and 10% BTS are applied, the EPC constant is 0.939, and the Tc can be boosted to 35.2 K, which is higher than those of the pristine T-graphene and many other 2D carbon-based superconductors.