Ali Qushji was born in 1403 in the city of Samarkand, in present-day Uzbekistan . His full name at birth was Ala al-Dīn Ali ibn Muhammed al-Qushji. The last name Qushji derived from the Turkish term kuşçu - the falconer - due to the fact that Ali's father Muhammad was the royal falconer Ulugh Bey .
Ulugh Beg Observatory - Landmark of Ali Qushji's career
He attended the courses of Qazi zadeh Rumi Ghiyāth al-Dīn Jamshīd Kāshānī and Muin al-Dīn Kashi. He moved to Kerman, Iran (Persia) and there he conducted some researches on the storms of Oman sea. He completed Hall-e Eshkal-i Ghammar (Explanations of the Periods of the Moon) and Sharh-e Tajrid in Kirman. He moved to Herat and taught Molla Cami about astronomy (1423). After professing in Herat for a while he went back to Samarkand and herald his works about moon to Ulugh Beg. Ulugh Beg was fascinated with the works and read the entire work while standing up. Ulugh Beg assigned him to Ulugh Beg Observatory which was called "Samarkand Observatory" at that time. He worked there till Ulugh Beg was assassinated.
After Ulugh Beg's death, Ali Qushji went to Herat, Tashkent and finally Tabriz, where around 1470, the Ak Koyunlu ruler Uzun Hasan sent him as a delegate to the Ottoman Sultan Mehmed II. At that time Husayn Bayqarah had come to reign in Herat but Qushji preferred Constantinople rather than Herat because of Sultan Mehmed's attitude toward scientists and intellectuals.