Our aim in the present study is to search for static spherically symmetric wormhole solutions in generalized Rastall gravity (GRG). In this theory, a varying coupling parameter can be regarded as the source of dark energy (DE) and hence, responsible for the current accelerated expansion of the Universe. We assume an anisotropic energy momentum tensor (EMT) with a linear relation between energy density and pressures profiles, i.e., pr(r) = w1rho(r) and pt(r) = w2rho(r), and obtain two classes of solutions to the field equations of GRG, including the solutions with zero and nonzero redshift functions. For these solutions we find that the matter distribution obeys the physical reasonability conditions, i.e., the flare-out, the weak (WEC) and null (NEC) energy conditions either at the throat and beyond it. These conditions put restrictions on model parameters, e.g. the equation of state (EoS) parameters and the value of energy density at the throat. Hence, we find that in the framework of GRG, asymptotically flat wormhole configurations can be built without resorting to exotic matter. We further study properties of timelike as well as null geodesics for the obtained wormhole solutions. In the case of null geodesics, gravitational lensing effects are discussed and it is shown that the throat of wormhole can effectively act as a photon sphere near which the light deflection angle takes arbitrarily large values.
