A recently introduced seeded dimension reduction approach enables existing sufficientdimension reduction methods to be used in regressions with n < p. The dimension reduction is accomplished through successive projections of seed matrices on a subspace to contain the central subspace. In the article, we will develop a seeded dimension reduction for multivariate regression, whose responses are multi-dimensional. For this we suggesttwo conditions that the dimension reduction is attained without the loss of informationof the central subspace. Based on this, we construct possible candidate seed matrices. Numerical studies and two data analyses are presented.