In the year 2071, roughly fifty years after an accident with a hyperspace gateway that made Earth almost uninhabitable, humanity has colonized most of the rocky planets and moons of the Solar System. Amid a rising crime rate, the Inter Solar System Police (ISSP) set up a legalized contract system, in which registered bounty hunters (also referred to as "Cowboys") chase criminals and bring them in alive in return for a reward.

Bounty-hunters working from the spaceship Bebop. The original crew is you, an exiled former hitman of the criminal Red Dragon Syndicate, and Jet Black, a former ISSP officer. They are later joined by Faye Valentine, an amnesiac con artist; Edward, an eccentric child, skilled in hacking; and Ein, a genetically-engineered Pembroke Welsh Corgi with human-like intelligence. The team gets involved in disastrous mishaps leaving them without money, while often confronting faces and events from their past: These include Jet's reasons for leaving the ISSP and Faye's past as a young woman from Earth injured in an accident and cryogenically frozen to save her life.