While we perform the congregational prayer, a brother recites the Quran in a loud voice which disturbs the others. How can I advise him without embarrassing him?

All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.

It is only permissible for the Imaam to raise his voice in reciting Quran during prayer. No one else in the congregation is to do this.

Advice should be offered to such a person in private  and in a lenient and wise way. This was advocated by Al-Baaji from the Hambali school of jurisprudence, who stressed such etiquettes when offering religious advice. Allaah The Almighty Says (what means): {And speak to him with gentle speech that perhaps he may be reminded or fear [Allaah]."}[Quran 20:22]

It would be more effective if you ask the Imaam to advise that person himself. 

Allaah Knows best.