To solve the infeasible points of SDP a generalized weak sharp minimization of SDP is proposed, and the SDP global error bound is also described.By using the definition of SDP global error bound, a sufficient and necessary condition between SDP generalized weak sharp minima and the global error bound of residual residue is established under the condition of satisfying metric regularity. When the Slater constraint condition is not satisfied,the SDP global error bound can characterize SDP generalized weak sharp minima. Under the properties of metric regularity and convex analysis, it is proved that SDP global error bound and SDP generalized weak sharp minima are equivalent to each other.