Your sentence:
If his words are true is suspicious.
I suggest you expand the sentence. As it stands, its wording is awkward. Here are some suggestions:
His words may be true, but I find them suspicious.
I find his words to be suspicious.
While he claims his words are true, I find them suspicious.
Though he claims his words are true, I find them suspicious.
I suspect his words--that he claims are true--are not true.
I suspect his words are untrue.
If you choose to use a word that is similar in meaning to suspicious, I suggest--thanks to contributor FumbleFingers--you use the word doubt(or doubtful). For example:
As for starting the sentence with the "if clause," I suggest you try a different approach. You could say,
- If his words are true, well, I sincerely doubt it.
That sentence is possible, but it is unnecessarily wordy.