You can suppress the adrenaline response by developing more effective coping skills, or learning more effective relaxation techniques. When you have anxiety and stress, your adrenaline response become overactive. So the way to suppress this overactive adrenaline response is to deal with your stress and anxiety. Learning coping skills like CBT(cognitive behavioral therapy) can be helpful. Also, learning relaxation techniques can be helpful to suppress your adrenaline response. Another way to suppress your adrenaline response is to consider natural anxiety supplements, such as KalmPro.