To the extent that one is afraid of dying, he or she is also afraid of living, because the two are inextricably intertwined. Life and death are two sides of the same coin. All beings are born and all being die.
Perhaps all of us fear death to some extent. However the fear of death isn't really the problem. Rather, the problem is our unwillingness to accept the fear of death. When we don't accept this fear, we tend to spend an inordinate amount of time and energy trying to banish it. Some people seek to overcome the fear by challenging it, imagining that by engaging in extremely dangerous activities it will go away. Others run from the fear, shrinking their lives down smaller and smaller, trying to avoid any danger. Both of these strategies keep us bound to the fear, so that the fear runs our lives.
The better way is to accept the fear, and to let love, joy, and clarity lead our life rather than our reaction to the fear of death.
The first step in this direction is to become aware of our relationship with the fear of death. Here's a way: Over the next week, simply notice how you react to thoughts of death. Do you notice any fear? If so, do you push the fear away, run headlong into the fear, or simply feel the fear and not make it the most important consideration? Simply notice what you do. This is the first step toward cultivating a wise and balanced attitude toward the fear of death.
Interestingly, many people who've been told that they have a limited time to live, and know death is imminent, accept the fear of death and are able to live more in the moment. By being aware of your relationship with the fear of death, you too can find greater aliveness in your life.