We study the cosmological behavior of locally rotationally symmetric (LRS) Bianchi type-I universe model in f(R,Tψ) gravity. For this purpose, we evaluate Hubble parameter, effective equation of state parameter (ωeff) and potential of scalar field (ψ) as a function of time using the assumption H=W(ψ). The behavior of these parameters is investigated for different models of W(ψ). It is concluded that exponential form of W(ψ) leads to time independent ωeff which corresponds to different stages of evolution while for the other two models, they correspond to stiff fluid stage. •We have studied anisotropic behavior of the universe through LRS Bianchi type-I model in the context of f(R,Tψ) gravity.•We evaluate H, ωeff and V(ψ) through the first order formalism for scalar fields.•We have investigated the behavior of these parameters for different values of W(ψ).•We conclude that exponential model of W(ψ) can explain the evolution of Bianchi type-I universe as compared to other models.