In this work, a non-singular spherically symmetric charged anisotropic stellar object has been obtained in the context of f(R,T)-gravity theory. The field equations in modified f(R,T) gravity are derived by taking f(R,T)=R+2χT and Lagrangian matter Lm=−(pr+2pt)3. The obtained field equations have been solved by taking MIT Bag model equation of state (EoS) together with Tolman–Kuchowicz ansatz (Tolman, 1939; Kuchowicz, 1968) in (3+1)-dimensional spherically symmetric space–time. The constants are determined by matching the interior spacetime with the exterior Reissner–Nordström at the boundary. Moreover, in order to verify the physical validity and stability of our proposed model, we investigate some important physical properties, such as effective pressures, effective energy density, energy conditions, TOV equations and sound velocities for different χ. In addition, the stability of the solution is tested by using cracking concept and relativistic adiabatic index. The compactness relation and surface gravitational redshift for f(R,T) stellar model are also discussed for the obtained solution. From our present study, it is observed that all our obtained results lie within the physically accepted regime which indicates the viability of our current solution for strange star model in the context of modified f(R,T) gravity theory.