Minimalist Grammars are a rigorous formalization of the sort of grammars proposed in the linguistic framework of Chomsky’s Minimalist Program. One notable property of Minimalist Grammars is that they allow constituents to move during the derivation of a sentence, thus creating discontinuous constituents. In this paper we will present a bottom-up parsing method for Minimalist Grammars, prove its correctness, and discuss its complexity.