Recently the teleparallel Lagrangian density described by the torsion scalar T has been extended to a function of T. The f(T) modified teleparallel gravity has been proposed as the natural gravitational alternative for dark energy to explain the late time acceleration of the universe. In order to reconstruct the function f(T) by demanding a background LambdaCDM cosmology we assume that, (i) the background cosmic history provided by the flat LambdaCDM (the radiation ere with Omega eff = 1/3 , matter and de Sitter eras with Omega eff = 0 and Omega eff = −1 respectively) (ii) the radiation dominate in the radiation era with Omega 0r = 1 and the matter dominate during the matter phases when 0m = 1. We find the cosmological dynamical system which can obey the LambdaCDM cosmic history. In each era, we find a critical lines that, the radiation dominated and the matter dominated are one points of them in the radiation and matter phases, respectively. Also, we drive the cosmologically viability condition for these models. We investigate the stability condition with respect to the homogeneous scalar perturbations in each era and we obtain the stability conditions for the fixed points in eacheras. Finally, we reconstruct the function f(T) which mimics cosmic expansion history
