It is better for him not to do that, and to listen attentively to the recitation of his imam. 

Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allaah have mercy on him) was asked: What is the ruling on the person praying behind the imam holding the Mushaf during Taraweeh prayers? 

He replied: 

I do not know of any basis for that. It seems that he should focus with proper humility and not hold the Mushaf, rather he should place his right hand over his left as is the Sunnah, placing the right hand over the left wrist and forearm and placing them over his chest. This is the most correct view and is best. Holding the Mushaf will distract him from these Sunnahs, and his heart and eyes may become busy following the words on the pages and that may distract him from listening to the imam. What I think is that not doing that is the Sunnah, and that he should listen attentively and not use the Mushaf. If he has knowledge he will be able to prompt his imam, otherwise others will prompt him. Then if it so happens that the imam makes a mistake and is not corrected, that does not matter, unless it is in Soorat al-Faatihah, rather it matters only in Soorat al-Faatihah, because al-Faatihah is a pillar of the prayer which is essential. But if he omits some verses other than al-Faatihah, that does not matter if there is no one behind him who can alert him to that. If someone holds the Mushaf to correct the imam in the case of necessity, then there is nothing wrong with that. But if each person holds a Mushaf, that is contrary to the Sunnah. End quote. 

He was also asked (may Allaah have mercy on him): 

Some members of the congregation follow the imam’s recitation in the Mushaf when he is reciting. Is there anything wrong with that? 

He replied: 

It seems to me that this should not be done. It is better to concentrate and focus on the prayer, and to place the hands on the chest and ponder what the imam is reciting, because Allaah says (interpretation of the meaning): 

“So, when the Qur’aan is recited, listen to it, and be silent that you may receive mercy”

[al-A’raaf 7:204] 

“Successful indeed are the believers.

2. Those who offer their Salaah (prayers) with all solemnity and full submissiveness”
[al-Mu’minoon 23:1]

And the Prophet (peace and blessings of Allaah be upon him) said: “The imam has been appointed to be followed, so when he says takbeer, then say takbeer, and when he recites, then listen attentively.” End quote. 

Majmoo’ Fataawa al-Shaykh Ibn Baaz, 11/340-342 

See also the answer to question no. 10067. 

And Allaah knows best.