The crime thriller premiered in August 2012, but its four-part run was interrupted following a real-life tragedy involving two female police officers.
The final episode - which featured scenes of a violent attack on a female police officer - was delayed by three weeks, attracting 1.9m viewers - considerably down from the previous episode's 4.39m.
Brown, who played tortured cop John Paul Rocksavage, revealed on Twitter that a second run is "not happening".
Good Cop followed Rocksavage as he pursued a violent quest for revenge following the brutal murder of his partner (Tom Hopper) by a gang of criminals.
Brown will next be seen reprising his role as Justin Ripley in the third series of Luther, which is currently filming and will air on BBC One later this year.
> Good Cop Warren Brown Q&A: 'The show's a thrill, dark, gritty'
Watch a trailer for Good Cop below: