Should I use a self-designed Block Cipher Mode of Operation? We all know we should NOT roll our self-designed encryption algorithm, how about block cipher mode with a certificated cipher method like AES? Will a self-designed block cipher mode cause any flaws or weakness to the cipher? 

I have search over the Internet but can't find a answer. Hope here is the right place to ask such a question.
Similar concerns apply as to any self-designed cryptographic algorithms. Standard block cipher modes usually have security proofs. If yours does not then even if it seems correct you may be missing some weakness.

An example of where security proofs of cipher modes are clearly important is the CCM mode (pdf). The same cipher key is used both for CBC-MAC authentication and to produce the CTR blocks used for encryption. This key-reuse is generally a bad idea and in a home-baked mode could be a weakness, but is proved safe in the particular composition used.

Very simple modes may be easy to prove secure yourself. However, I doubt those have any real advantages over using a standard mode either.