In this research, we have studied magnetized strange quark matter (SQM) solutions for Friedmann-Robertson-Walker (FRW) universe in f(R, T) gravity. To obtain exact solutions of modified field equations we have used f(R, T) = R + 2 f(T) and f(R, T) = f(1)(R) + f(2)(T) models given by Harko et al. (Harko et al. in Phys. Rev. D 84: 024020, 2011) and f(R, T) = R + f(3)(T) model (here f(3) is an arbitrary function) with cosmological constant Lambda. For t -> 8 we obtain p = -rho dark energy situation with small constant values of cosmological constant in three different f (R, T) gravitation models. In our solutions magnetic field does not observe also we have transformed our solutions from FRW universe to Static Einstein Universe (SEU) and we get f(R, T) gravity results for SEU universe. Finally we discussed our physical solutions. (C) 2016 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved.