The Reciting of Holy Quaran is allowed in between the time of Asar & Maghrib.

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.

Reciting the Quran is permissible at all times of day and night. Abu Hurayrah   reported that the Prophet, sallallaahu ‘alayhi wa sallam, said, "There is no envy except in two (cases): A man whom Allaah has taught the Quran and he recites it during the hours of the night and during the hours of the day, and another man listens to him and says, 'I wish I had been given what has  been given to so-and-so, so that I might do what he does'; and a man whom Allaah has  given wealth and he spends it on what is just and right. Whereupon another man may say, 'I wish I had been given what so-and-so has been given, for then I would do what he does.'" [Al-Bukhari]

There is no evidence forbidding reciting of the Quran at any time unless there is an impediment such as Janaabah (major ritual impurity) and the like.

However, what is actually forbidden during the period between ‘Asr and Maghrib prayer is the supererogatory (voluntary) prayer that has no reason (See Fatwa 88125).

Allaah Knows best.