In this article I consider the convergence of the Eilenberg-Moore spectral sequence for Morava K-theory. This spectral sequence can be constructed by applying Morava K-theory to D. L. Rector's geometric cobar construction of the Eilenberg-Moore spectral sequence. I have shown that the Eilenberg-Moore spectral sequence for Morava K-theory converges if the Eilenberg-Moore spectral sequence for ordinary homology collapses at E² and the homology satisfies certain finiteness conditions.