The EU Global Human Rights Sanctions Regime of 2020(GHRSR) establishes a sort of “universal” extraterritorial jurisdiction by sanctioning persons or entities who commit serious human rights violations and abuses around the world. However, the principle of universality in customary international law cannot support the validity of the EU GHRSR’s extraterritorial jurisdiction uncontroversially, for there are considerable divergences in present state practices. The unilateral extraterritoriality of the EU GHRSR may offend the sovereignty of the third states and violate the non-intervention principle, and may also slide into a danger of abusing the right. Furthermore, the EU institutions shall state the reasons for its making sanctions against certain persons or entities under the obligations of EU human rights law. According to the case law established by the EU Courts, some sanction measures taking under the EU GHRSR may be challenged for failing to base themselves on a sufficiently solid fact.