Joseph McManus, from Orchard Hill, Crumlin, who had been on compassionate bail for his brother's funeral, was also told, that when the authorities decide it is safe to free him, he will serve an extended five-year period on supervised licensed parole.
Defence lawyer Neil Fox said an apologetic 28-year-old McManus, who believes his brother's killers were trying to get at him, "simply could not deal with his grief" and "lost control" when his dangerous driving injured the policeman, on 6 April last year.
Mr Fox said that McManus had panicked because he was unlawfully at large, but now wished to apologise to the injured officer and also to the court, because he felt "particularly bad" as he had been on compassionate bail at the time.
"It was an act of desperation...really a cry for help," he added.
His 26-year-old brother Kieran was gunned down outside Domino's pizza takeaway shop at Kennedy Way, Andersonstown, on Easter Saturday night 2013 by a lone masked gunman as he was about to head out on a delivery run.
On Monday Belfast Recorder Judge David McFarland told the victim's older brother that with 176 previous convictions, mostly road traffic, but also involving assaults, kidnapping, robbery, possession of an offensive weapon and making threats to kill, he had an appalling record, which was a further aggravating factor.
The Crown Court judge added that McManus presented a significant risk of re-offending in the future, and in the circumstances he regarded him as posing a serious risk to the public.
In all, McManus pleaded guilty to two separate sets of offending, beginning in October 2011 when involved in series of robberies of several students as they walked home from a night out, and then in the driving offences while out on compassionate bail for his brother's funeral last April.
Judge McFarland said with regard to the robbery charges he had played a secondary role as a driver, but he was part of a joint enterprise and as such must accept responsibility for the actions of others who used violence, and offered violence, to the group of students robbed on the Malone Road.
The judge added, however, that for his involvement in attempting to escape apprehension while on bail, he would have to take primary responsibility for, which was also an aggravating matter.
Earlier, prosecution lawyer David McAughey told the court that police had been alerted to the hijacking of a car which was later found burnt out in the Hannaghstown Hill area.
As police arrived on the scene, "those responsible" made off in a silver Renault Megan, which was later spotted in the nearby car park of the Suffolk Inn on the Suffolk Road.
Mr McAughey said as an officer attempted to snatch the keys from the ignition, McManus drove off, with the officer still clutching on to the door of the car.
At one point McManus drove at a police Land Rover and the officer received several "crushing injuries", fracturing a number of his ribs.
He added that the officer escaped further injury when another policeman got in the passenger door, and spun the steering wheel round, before managing to drag McManus out of the car.