A good word to use in many different ways is "kind". You are being so kind. You are being too kind. You are so kind. You are really too kind. You can (and probably should) start or end each one of those with "thank you". Thank you, you are so kind. You are being too kind, thank you.

Yeah, I agree with the above answers. It's really best to just accept it with a "thank you" or "thanks" to avoid false modesty. (Like when you say "No I'm not" or "Not at all" when really you are those things) Just be gracious. "I appreciate that" is another, perhaps less direct way of saying "thank you" "That's nice of you to say" is acceptable as well if you really don't want to "agree" or say "thanks"

Culturally speaking, I think it is perfectly modest to accept a compliment in this way. You can say 'thanks' as well as 'thank you.' However, if you still feel uncomfortable in using this response, you can also say 'I try.' This might mean that you are grateful that they recognize your hard work in learning English. However, depending on the situation, it might imply that you are proud as well. This could get complicated in some situations and I really would not recommend using it. All in all, the safest way to accept the compliment would be to thank a person. Don't worry about sounding proud! You should be proud that you have accomplished the feat of becoming good at speaking and writing in English! Sorry if this doesn't answer your question :/

Brenna.jaline, you're right. One of cultural difference between Japan and the west is that how you accept compliment. Modest way of speaking, behavior is sometimes considered to be good here. This thoughts won't be away from me even if I know western society is not like that. (sign lol) So this question is compromising for me rather than simply accepting it in order to manage my feelings. Sorry for long explanation. I really appreciate everyone's help here.

As you can see, there are many ways to receive a compliment. The key is to avoid false modesty.