I will show how toconstruct `Newton-Cartan Supergravity’ , a non-relativistic version ofsupergravity, by applying a gauging procedure to the supersymmetric Bargmannalgebra. As a warming-up I will discuss the relativistic and the bosonic casesfirst. So far the construction has only been performed in three spacetimedimensions. I will comment on the superparticle in a Newton-Cartan supergravitybackground.