In this article the relations between superprojective properties and local superpro- jective propcrtics of Banach space are discussed. For a reflexivc Banach space X, it is proved that X is lp-subprojective space if and only if X* is lp-superprojective space, X is local lp-sub- projective spacc if and only if X* is local lp-superprojective space and X is local subprojective space if and only if X* is local superprojective space, where 1/p+1/q=1.