Cosmological implications of a generalized Rastall theory where the non-conservation equation is promoted to accepts arbitrary functions of the Ricci scalar is considered. We have obtain the model parameters of the power-law ansatz f ∝ R η , using H0 and f σ8 data sets and show that the generalized Rastall theory could satisfy observational data. The dynamical analysis of the model shows that for η ∈ (0, 1), the dust dominated fixed point is lost and as a result the parameter range of η should be restricted to η ≥ 1. We will also show that the genralized Rastall theory will predict more accelerating universe with larger radius, compared to the ΛCDM model.