We studied the vertex distinguishing edge coloring of Kn(n≥20, n≡0(mod2)) graph with four independent edges deleted, and obtained the vertexdistinguishing edge chromatic number of Kn-{v1v2,v3v4,v5v6,v7v8}(n≥20, n≡0(mod2)), where Kn-{v1v2,v3v4,v5v6,v7v8} is denoted by the complete graph with order n deleted edges {v1v2,v3v4,v5v6,v7v8} of Kn.