The mother of the great sage (Vyasadeva) was Satyavati the daughter of the Vasu (fisherman), and the father was the great Parasara Muni. That is the history of Vyasadeva's birth
SB Canto 1
Sūta Gosvāmī said: When the second millennium overlapped the third, the great sage (Vyāsadeva) was born to Parāśara in the womb of Satyavatī, the daughter of Vasu.
There is a chronological order of the four millenniums, namely Satya, Dvāpara, Tretā and Kali. But sometimes there is overlapping. During the regime of Vaivasvata Manu, there was an overlapping of the twenty-eighth round of the four millenniums, and the third millennium appeared prior to the second. In that particular millennium, Lord Śrī Kṛṣṇa also descends, and because of this there was some particular alteration. The mother of the great sage was Satyavatī the daughter of the Vasu (fisherman), and the father was the great Parāśara Muni. That is the history of Vyāsadeva's birth. Every millennium is divided into three periods, and each period is called a sandhyā. Vyāsadeva appeared in the third sandhyā of that particular age.