He studied under Johann Sebastian Bach at the Leipzig Thomasschule; played for ten years (1748-1758) under A. Hasse in the band formed at Dresden by the elector of Saxony; and then, going to England, became (in 1759) chamber-musician to Queen Charlotte. He gave a concert of his own compositions in London, performing on various instruments, one of which, the pentachord, was newly invented.
In 1762 Johann Christian Bach, the eleventh son of Johann Sebastian Bach, came to London, and the friendship between him and Abel led, in 1764 or 1765, to the establishment of the famous concerts subsequently known as the Bach and Abel concerts. For ten years these were organized by Mrs Comelys, whose enterprises were then the height of fashion.
In 1775 the concerts became independent of her, and were continued by Abel unsuccessfully for a year after Bach's death in 1782. At them the works of Haydn were first produced in England. After the failure of his concert undertakings Abel still remained in great request as a player on various instruments new and old, but he took to drink and thereby hastened his death.
He was a man of striking presence, of whom several fine portraits, including two by Thomas Gainsborough, exist.