Abdullah Ibn Mesud is the Sahaba (companion of the Prophet Muhammad (PBUH)) who read the Quran aloud first.

When Abdullah Ibn Mesud became Muslim, Muslims could not openly perform their worships along with our Prophet (PBUH) and could not recite aloud the Quran. Such an act of Muslims provoked the ignorantly behaviors of Mushriks (polytheists) and made them to attack criminally and violently on Muslims. Therefore, Muslims to preserve themselves from the danger of polytheists, they abstained from the behaviors that agitate polytheists against them. Thus, in those hard days Abdullah Ibn Mesud wanted to recite Quran in the Ka’bah. Our Prophet (PBUH) and his companions told him that it was a dangerous act, there wasn’t a powerful family with him in Mecca to protect him and polytheists would act cruelty against him and torture him, but with his exalted faith he dealt with all these troubles and he said “Allah protects me from their cruelty” and went to the Ka’bah.
At the same time the elder polytheists of Quraysh assembled in Harem and discussed on a topic. While they were discussing, he (Abdullah Ibn Mesud) recited Bismillah firstly and started to read surah Ar-Rahman from the Quran with a fascinating voice. Everybody was astonished and when they turned towards him to find out who this brave man was, they realized that he was Abdullah Ibn Mesud. Polytheists of Quraysh got angry with him and wanted to punish him with a severest punishment. They laid him down on a hot desert and forced him to abandon the Islam religion. But Ibn Mesud never paid even the least little bit attention to their punishment. They set him free when they realized that punishment will not change his mind. 
Abdullah Ibn Mesud became sick because of such disloyal behavior of polytheists, but his exalted light of belief and spirituality never died down. At the earliest opportunity, Ibn Mesud did the same act, near the assembly of the Quraysh’s polytheists he recite the Quran with his loudest voice again, so he is the one who conveyed Islam to the polytheists by reciting the Quran aloud first in the Ka’bah after our Prophet Muhammad (PBUH). (Ibnu’l-Esir, Usdu’l-Gabe, III, 256-257)