Fear of failure is a reality. We often don't try things because of the fear that we could fail. You can pretend that you are not afraid of failure but you have real reasons for not doing what you need to do in order to succeed. But pretending to be not afraid will not make your fear go away. Nor will it prod you to act. So, the very first thing to do to overcome the fear of failure is to accept that you have, in fact, have this fear which is holding you back.
Once you accept you have the fear, you can think of ways of overcoming it. There are broadly two ways of overcoming the fear of failure. One is to make your desire to succeed weigh more than the fear of failure. But how to do this? You can make the desire to succeed stronger by creating a strong motivation. This can be done by dwelling on the good things that success will bring you. I know that this is easier said than done. But motivation itself is being a vast subject with innumerable approaches, I can't elaborate on the ways by which you can motivate yourself in this post. You will, perhaps, see powerful tips on motivation in other posts.
The second way to overcome the fear of failure is using a bigger fear. If the fear of the consequences of not doing the thing is greater than the fear of doing a thing, then you will do it! If you are afraid of swimming, you may be standing on the edge of a swimming pool for hours together, not venturing to dive into water. But if your swimming coach threatens to bash your back with a club if you stand there for more than 30 seconds, then you will jump into the water well ina dvance of the deadline, won't you?