Kammala jumla mai zuwa: A watan Maris na 2011, an sanar da cewa Griffin ya sanya hannu kan yarjejeniyar shekara biyu tare da lardin kuma zai kasance wani ɓangare na tawagar farko don kakar wasa mai zuwa. Connacht ya buga wasan Heineken Cup a karon farko a gasar 2011<unk>12, tare da Griffin yana wasa a wasanni uku daga cikin wasanni shida na lardin. Ya fara a wasan waje da Harlequins, wasan gida da Toulouse da wasan waje da Gloucester. Ya kuma buga wasanni 11 da sau hudu a gasar
wannan shekara ta gasar.