Islam permits to give birth more than one child but on the other hand today is population explosion.

It is a wrong conception that Islam preaches giving birth to many children. There is a Hadith in Sahih al-Bukhari. One Sahabi tells us: We were observing birth control (azl) at the time of the Prophet of Islam, but the Prophet never prohibited it. Also, no verse was revealed in the Quran in this regard.