We construct and study supersymmetric extension of the Einstein-aether gravitational theory. Using superfield formalism we carry out unique linearized Lorentz violating supergravity action invariant under super-gauge transformations and obtain its bosonic part expanding in the Grassman coordinates. The model is considered also at the component level. We study supercurrent supermultiplet in the theory as an alternative way to prove its uniqueness and to construct fermionic interaction in the model. The phenomenological consequences of the theory and experimantal constraints on the coupling constant are also discussed.