In this article, we have investigated the behaviors of magnetized strange quark matter distributions for Bianchi I and V universes in reconstructed f (R, T) = alpha R-1+alpha(2)f(3)(T) gravity (here alpha(1) and alpha(2) are constants; f(3) (T) is an arbitrary function of T). To get solutions of the field equations we have used a deceleration parameter and the equation of state for strange quark matter. The new represented f (R,T) model includes two models of Harko et al. and transforms to general relativity. When t ->infinity, we get the dark energy model (p = -rho) in reconstructed f (R, T) = alpha R-1 + alpha(2)f(3)(T) gravity. However, we obtain zero magnetic field in all f (R,T) gravitation models.