My parents know that I'm dating someone but they don't know he's black (I'm white). I'm afraid of telling them because I'm worried about their reaction. How can I approach them and discuss this?

I will assume you are underage. Have your parents expressed any disapproval of interracial couples in the past? Have they forbidden you from dating people of other races? The answers to these questions determine how you should approach them.
If you KNOW your parents will disapprove:
Calmly explain to your parents that you developed a friendship with a boy of another race and that you are now dating. Explain that you know they will object, but you have never understood their reasons for objecting and you would like them to meet him and judge him according to his individual qualities rather than any stereotypes they may have formed. Tell them it would mean a lot to you to do this. I think it's very important to keep your cool - no shouting or name calling.
I'm warning you that this probably won't work the way you'd like it to - I wouldn't be surprised if you end up grounded. However, it is important that if you make a decision to date someone your parents dislike for ANY reason, it is best to be honorable about it if you believe you are in the right, and take the consequences.
If your parents have never expressed an opinion on this issue:
Get your parents together and again explain that the person you've been dating is black, and you want them to know that before meeting him. Tell them what you like about him and say that you hope they will see those same qualities in him. Ask when it might be a good time to have him meet them.
If your parents have always taught you that all people are "the same" and that prejudice against any race is wrong, take the same steps as if they had never expressed an opinion.
You have to remember that in their house, it is their rules which prevail. Sometimes this is extremely unfair and difficult, but it is a fact everyone under 18 has to live with, for a few more years anyway. I went through this myself and was surprised to find out how supportive my parents were - I hadn't given them enough credit. I hope you will also be pleasantly surprised!

It really depends on your parents. Some parents don't respond well to just being bluntly told something. Ease it on them and make sure that they are alright with it.

I am white as well, dating a black guy that is not only black, but of a different religion. There are so many things that fight against us, but you really have to discuss things thoroughly with your man and your parents.

You are not being true to yourself or your boyfriend and that's not right...........

If you truly care about this man, your parents are just going to have to accept who you care about. Let them know your dating a wonderful man who just happens to be dark skinned. If you are mature about it, your parents will have to be the same whether they like it or not.

Talk to them, if you are afraid to talk with them, you should sort out whatever problems you have with them before telling them of your interracial dating!!!

Here's a thought: Just don't tell them.

I'm not trying to be flip. Consider holding off until they actually meet him, at which point they are obgliged to be polite and they will get a chance to know him as a person. If you tell them beforehand, they might dismiss him out-of-hand and forbid you from seeing him.

I'm sure that there are plenty of other irrelevant things about him that you wouldn't mention to your parents before they meet him. Why should his skin color be any differant?