There is nothing wrong with reading from the Mus’haf in Taraweeh prayer. ‘Aa’ishah (may Allaah be pleased with her) had a slave who used to lead her in prayer in Ramadaan, reading from the Mus-haf. Narrated by al-Bukhaari in a mu’allaq report (1/245).
Ibn Wahb said: Ibn Shihaab said: The best of us used to read from the Mus-haf during Ramadaan. Al-Mudawwanah, 1/224.
Al-Nawawi said: If he reads from the Mus-haf that does not invalidate his prayer, whether he had memorized it or not. Rather he should do that if he has not memorized al-Faatihah, and if he turns the pages sometimes whilst praying that does not invalidate his prayer. … This is our view and the view of Maalik, Abu Yoosuf, Muhammad and Ahmad. End quote from al-Majmoo’, 4/27.
Sahnoon said: Maalik said: There is nothing wrong with the imam leading the people (in prayer) whilst reading from the Mus-haf in Ramadaan and in naafil prayers. Ibn al-Qaasim said: That is makrooh in the case of obligatory prayers. Al-Mudawwanah, 1/224.
With regard to those who object to that on the grounds that holding the Mus-haf and turning its pages constitute excessive movement, this is an invalid objection, because it is proven that the Prophet (peace and blessings of Allaah be upon him) led the people in prayer whilst he was holding Umaamah, his daughter’s daughter. Narrated by al-Bukhaari (494) and Muslim (543). Holding the Mus-haf whilst praying is not more serious than holding a small child whilst praying.
We have quoted the fatwa of Shaykh Ibn Baaz stating that this is permissible, in the answer to question no. 1255.
And Allaah knows best.