We study the behavior of cosmological parameters, massive and massless scalar fields (normal or phantom) with a scalar potential in f(R, T) theory of gravity for a flat Friedmann-Robertson-Walker (FRW) universe. To get exact solutions to the modified field equations, we use the f(R, T) - R + 2f(T) model by Harko et al. (T. Harko et al., Phys. Rev. D 84, 024020 (2011)), where R is the Ricci scalar and T is the trace of the energy momentum tensor. Our cosmological parameter solutions agree with the recent observational data. Finally, we discuss our results with various graphics.