What is the Zoroastrian holy book called?

The Zoroastrian holy book is called the Avesta.

More precisely, the Avesta is a corpus, or collection, of sacred Zoroastrian writings rather than a single book composed at one time. Its texts are written in Avestan, an ancient Iranian language, and preserve prayers, hymns, ritual instructions, laws, and religious teachings. The Gathas, traditionally attributed to Zoroaster, are among its oldest and most important sections.

The main parts include the Yasna, used in central liturgy; the Visperad, which supplements the Yasna; the Vendidad, containing ritual and purity regulations; and the Yashts, hymns devoted to various divine beings. The Khordeh Avesta is a shorter prayer collection used by many worshippers.

A common mix-up is treating the Avesta as a complete original library. Zoroastrian tradition speaks of 21 nasks, or books, but much of that larger collection was lost. The surviving material was transmitted orally for centuries, and the Avestan alphabet was developed during the Sasanian period, from 224 to 651 CE.