Two teenagers and a young man have been charged with the murder of a Brisbane GP shot dead at his home last week.

Dr Luping Zeng, 56, was packing his car with the garage door open when he was shot in the chest. He later died at Princess Alexandra Hospital.

Police believe the three accused did not know Dr Zeng and robbery was the likely motive behind the killing.

A 17-year-old boy, who cannot be named for legal reasons, was arrested in Slacks Creek on Thursday afternoon.