I have seen many people holding Qur'an while praying Taraweeh. I want to know if it is a allowable or not?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

It is lawful for both the Imam and the one praying behind him to read from a Mus-haf during Prayers including the Qiyyam (night Prayer). There are many pieces of evidence for this ruling. The most explicit evidence is the Hadeeth reported by Al-Bukhari from ‘Aa’ishah which mentions that Thakwaan - ‘Aa’ishah slave - used to pray as her Imam reading from the Mus-haf.

But if one can recite the Quran from memory that is better. As for holding the Mus-haf for the one praying behind the Imam, it is not desirable as it is not reported from any of the Salaf (rightly guided predecessors). Such an act may also cause the praying person to leave the Sunnah of putting the right hand on the left hand on the chest in the prayer, which is a Sunnah.

Allah knows best.