From the incredible Steph Davis, climber, BASE jumper, wingsuit flyer, blogger and writer:
The best way to dull fear is to practice repetition. The more times you are in an environment or situation you find scary, the less it will intimidate you.
Every time you put yourself in an intimidating situation, even if you don’t actually do much (i.e., you take a 4 inch lead fall onto a giant bolt on purpose after alerting your belayer, instead of…taking soaring, monster whippers onto a blue TCU as you nearly get through the crux of your project), you are STILL making progress, and you should be happy, and keep at it.
The first time I started trying to free El Cap, I was terrified! Actually, when I started working on the Salathe headwall, I was also terrified. But I gradually got used to all the exposure, and was able to relax (somewhat) up there. Just keep at it.