In this paper, we have researched tachyon field, k-essence and quintessence dark energy (DE) models for Friedmann-Robertson-Walker (FRW) universe with varying G and A in f (R, T) gravitation theory. The theory of f (R, T) is proposed by Harko et al. [Phys. Rev. D 84, 024020, 2011]. In this theory, R is the Ricci scalar and T is the trace of energy-momentum tensor. For the solutions of field equations, we have used linearly varying deceleration parameter (LVDP), the equation of state (EoS) and the ratio between A and Hubble parameter. Also, we have discussed some physical behavior of the models with various graphics.