In this paper, such definitions as .D-η-properly prequasiinvex, and D-η-properly semistrictly prequasiinvex for vector-valued maps are introduced, under the lower D-Semi-continuous condition and the upper D- Semi-continuous condition, respectively. Some equivalent propositions concerning .D-η-properly prequasiinvex for vector-valued maps are obtained, and the relationsamong D-η-properly prequasiinvex, D-η-properly semistrictly prequasiinvex and D-η-properly strictly prequasiinvex are discussed. Under some conditions, the fact that the local weak efficient solution of (VP) must be the global weak efficient solution of (VP) is proved. These results generalize the corresponding results in [2, 6-9].