An interesting class of modified gravity theory has recently been proposed, namely, the Rastall-Rainbow gravity. This theory is a combination of two theories: the Rastall theory and the Rainbow description. The present work is devoted to explore the possibility of the existence of static spherically symmetric wormholes and present the full gravitational field equations. In particular, considering specific choices for the redshift and shape functions, we present exact solutions of asymptotically flat wormhole geometries. With the specific examples, we investigate some issues concerning energy conditions and adiabatic sound velocity. We also consider the “volume integral quantifier” to assess the total amount of energy-condition violating matter. Finally, we conclude that the violation of energy conditions may be alleviated by decreasing Rastall’s parameters and adjusting the Rainbow functions.