A fear of death is normal and natural — it's hardwired in us all through natural selection. Species that do not fear death don't tend to stick around very long I imagine, so it can be thought of as a selection pressure. It's primal.
It's important to keep this in mind: you'll only ever experience what it's like to be alive. You'll never experience "being dead" — there's no eternal darkness or void or whatever it is your imagination has led you to believe.
Life might be thought of as a party — a party has to end at some point. But do you know what would really suck? Spending the entire party worrying about it coming to an end. So, forget about it — it's out of your control and it's really nothing to be scared about. If you're still feeling irrational fear after reading our replies, I recommend reading a book by Greta Christina: https://www.amazon.com/Comforting-Thoughts-About-Death-Nothing-ebook/dp/B00QVLEQRU
OP, I would highly recommend you read a book that has helped a lot of people I know (who also had issues with a fear of death). I read it myself and have to say it's an indispensable resource. The author puts death into a really pleasant, yet rational perspective:
https://www.amazon.com/Comforting-Thoughts-About-Death-Nothing-ebook/dp/B00QVLEQRU
Greta Christina literally wrote the book on this topic.
An interesting perspective is that without death, I wouldn't be here. I exist because the germ line cells in my body want to propagate themselves. If they were immortal, they wouldn't need a complex, multicellular support mechanism to accomplish the goal of continuing on into the future, they'd just continue. That a few grams worth of germ line cells require tens of kilograms of me to propagate is a consequence of the inevitability of death. I am my ancestors' way of fighting death.
I'm glad it helped!
There's a book I'd recommend if you need further comfort:
https://www.amazon.com/Comforting-Thoughts-About-Death-Nothing-ebook/dp/B00QVLEQRU
Therapy might be a bit too far. I think reading a good book on the subject of death from an atheistic perspective helps tremendously: https://www.amazon.com/Comforting-Thoughts-About-Death-Nothing-ebook/dp/B00QVLEQRU
You've been conditioned to fear death, or more specifically, the horrible fate that awaits you since you don't believe in a god who requires your submission for you to earn eternal reward. The way to break any fear is to confront it and examine it whenever it hits you. What do you fear? Why do you fear it? What do others have to say on the topic? Our FAQ has a short topic on it and Greta Christina has recently come out with a new book on death.