We extend the Berkovits-Maldacena prescription for MHV amplitudes of the open superstring to the closed superstring, showing that in the alpha'aEuro parts per thousand= 0 limit it reduces to the result of supergravity found recently by Hodges. We also verify that this prescription calculates the correct superstring tree level MHV amplitude for 4 gravitons including alpha' corrections.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)