More details about my question:

As shown in the above screen capture, I think paragraph 1 and 2 had the same formatting, but why "The" had an indication that needs to be decapitalized?

I want something like paragraph 1,

A word with capitalized first letter in the middle of a sentence (after the heading), but without error indication.

It might be flagging it because of grammar rather than capitalization. Turn of grammar checking, Word Options>Proofing>Mark grammar errors as you type, then see if it still does it.

Turning off Word's grammar checking is a bad idea.

Word's grammar tools do not ordinarily apply capitalisation other than at the start of a sentence. Nor do they normally remove capitalisation. The green wavy line is only there because Word has detected a capitalised 'the' in the middle of a sentence. The 'in' would ordinarily have a green wavy line under it too. However, if you've already done a spelling/grammar check and told Word to ignore the rule once for 'In', the wavy underline won't show. If you do a spelling/grammar check and told Word to ignore the capitalisation rule wavy underline under 'The' won't show either.

__________________
Cheers,
Paul Edstein
[Fmr MS MVP - Word]

Thanks for all the answers and help.

At the moment, I still have the green line indication, but I think I know the reason of it. At the beginning, I thought it was a formatting issue, as there are first letter capitalized word in the middle of both paragraphs, and paragraph 1 doesn't have the green line. It makes me think that WORD might have a setting that allow the situation in paragraph 2, under the normal grammar & formatting checking rule. Because even if I turned off (or 'ignore') the checking indication, other people will still see it when they open the doc in their word.

Later of that, I tried different words at the highlighted area, and only some word combination didn't give the 'green line'. So I think it's a grammar issue, and there is no way to top WORD give the green line indication for this situation unless turn the checking off or 'ignore' it.

You can mark the text for "do not check spelling or grammar" through language settings. See Mastering the Spelling Checker for guidance on this.