In this study, we investigate homogeneous and anisotropic Bianchi type I universe in the presence of quark matter source in f (R, T) gravity (Harko et al. in Phys. Rev. D 84:024020, 2011) with cosmological constant A (where R is the Ricci scalar and T is the trace of the energy momentum tensor). For this aim we have used the anisotropy feature of Bianchi type I universe and equation of states (EoS) of quark matter. We explore the exact solution f(R, T)=R + 2f(T) model for Bianchi type I universe model. When t -> infinity, we get very small cosmological constant value, this result agrees with recent observations.