In this paper, we focused on the study of anisotropic strange stars with anisotropic matter distribution in the framework of f(T,T)=αT(r)2+βT(r) model, where α, β are arbitrary constants, T and T represent the torsion scalar and trace of energy–momentum tensor, respectively. This model has interesting cosmological properties, in addition to providing an effective dark energy sector explanation (Harko et al., 2014). In order to achieve our goal, we considered the Krori–Barua space–time and utilize the off-diagonal tetrad components for deriving the corresponding set of field equations. We calculate the relation for the evaluation of effective density, effective radial and tangential pressure using the EoS of strange star i.e., MIT bag model pr(r)=13[ρ(r)−4Bg]. The unknown constants appearing in the solution have been evaluated by using the conventional matching of interior and exterior space time. To check the feasibility of our proposed model we discuss the anisotropy, energy condition, TOV forces, abreu condition, EoS parameters, adiabatic index, mass function, compactness and redshift for different compact stars models namely, PSRJ1416−2230, 4U1608−52, CenX−3, EXO1785−248 and SMCX−1.