It is called "Thantophobia" or fear of death. It is extremely common and I feel so many phobias are really about this issue. I have a fear of flying? Why? heights but also...I fear dieing up there. Or down there as the case may be.
So you are not abnormal for your fear.
There is an article in the Chicago Tribune about this topic which I will invite you to read.
There is a ton of literature of how to deal with this particular fear. Here is one such article. And here is yet another where the author thinks that we can use our fear of death to grow emotionally.
Have you experienced a great emotional trauma? Where do your thoughts of death come from? Have you been to many funerals? How has death made an impact in your life.
I remember feeling very distressed by the thought of death when I was young too. It just seems so unfathomable. But really...it is just another natural aspect of life. We are so removed from it nowadays except to see brutality on the news...and so we have trouble thinking of it in any other way as frightening and traumatic.
I think too...the fear stems from feeling a loss of control. The way to combat this anxiety is to focus on right now. Right now you are alive and there is much which is under your control.
Sometimes phobias can be too much for us to handle alone. Would you be willing to talk to a counselor or therapist who might be better equipped to give you advice on how to handle this? Behavioral or cognitive therapy and even medication might be of help.
I am sorry you are going through this. Hang in there. And please come back to tell us how you are doing. Thank you for your question.