The footage shows Paul Archer, 40, shouting and swearing at English bull terrier Denver in the back of a parked car.
In the video, Archer threatens the animal with a hammer before slamming the boot when he fails to meet his demands to get out.
Archer was investigated after the mobile phone footage was sent to the RSPCA anonymously.
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RSPCA inspector Gemma Fowler said: “Watching the footage, it’s clear that Denver is frightened of the way his owner is behaving towards him.
“Mr Archer wants him to get out of the car, and is becoming increasingly angry and violent because he is refusing to do so, finally slamming the boot closed on him and shouting at him to ‘die’.
“We all get angry sometimes, but Mr Archer’s behaviour towards Denver is totally unacceptable.”
Archer, of Glensdale Road, East End Park, admitted failing to meet the needs of a dog by failing to allow him to exhibit normal behaviour when he appeared at Leeds Magistrates’ Court.
In mitigation, the court heard the defendant was cleaning the car when Denver jumped in and broke the screen on an iPad.
As well as the animal ban, Archer was given a 12-month community order and ordered to pay £750 costs. Denver will now be able to rehomed by the RSPCA.
Ms Fowler said: “Denver is a smashing dog with a great personality and happily he will now be able to go to the kind of home he deserves.
“I’d like to say thank you to the person who filmed and sent this footage to us, without which we wouldn’t have had a case. They have changed this dog’s life.”