Praise be to Allah.
Yes, it is permissible to pay zakat before its due date, because the Prophet (peace and blessings of Allah be upon him) accepted two years’ zakat in advance from al-‘Abbas ibn ‘Abd al-Muttalib. But we should remember here that the annual payment of zakat is worked out according to the Hijri (Islamic) calendar, and not the Gregorian (western) calendar – the difference between them is well known.