The existing literatures are lacking on the cost and benefit concerns, screening the measures and convergence of interval-valued triangular fuzzy numbers-grey relation analysis (IVTFN-GRA) weight together. Nonetheless, Green supply chain management is always suffering the linguistic preferences and system incomplete information in evaluation process to enhance the performance. Yet, those previous studies are merely based on un-converged weight results. Hence, this study proposed a hybrid method to dealing with this multi-criteria evaluation problem. Fuzzy Delphi method proposes to screen the evaluation criteria and converged IVTFN-GRA weight method handles the vagueness system uncertainty and incomplete information with interdependence relations. Hence, the proposed hybrid method enhanced the green supply chain management and compared multi-methods to enhance their performance in Taiwanese electronic focal firm. The result showed that the converged weight is consistent with the real practices, despite the differences with the current average weighting method. The finding in the long-term perspective: resilience and operational improvement are the top weighted aspects.