Errol McKenzie was shot three times from close range in Seymour Road playing fields in Leyton, east London, on April 11 2010 after sitting on a bench to eat food and have a drink he bought in a nearby shop.
While police said there is no obvious motive for the 37-year-old’s killing, there are a number of people captured on CCTV footage that they still want to trace.
Mr McKenzie’s daughter and nephew, Nicole Bent and Ty McKenzie, said their family was “still suffering and struggling” with their loved one’s murder and wanted closure.
Mr McKenzie said: “Just please, if you have any information, just come forward. My grandparents especially have been in pain for like 12 years, just let them rest now.
“Let closure come to our family. Nicole’s been suffering, my uncles, brothers, and sisters have been suffering. It’s time to close the case and let’s get justice and put this to bed now and let everyone move on in life.”
He added: “It’s been very hard on the family, especially Nicole and my grandparents as well because they don’t seem to understand like, why would someone do that to him?
“He’s a man of good character so it has been extremely difficult for us as a family and to this day we’re still suffering and struggling individually with the situation.”
Ms Bent said: “He’s friendly and he’s kind, and he’s caring. He always helped anyone who needs help and he was very loving and a father and to his family.”
On the night of his murder, Mr McKenzie, a repair man, had been to the Lee Bridge Road area of Walthamstow, Tottenham, and likely visited Northumberland Park, police said.
He was seen on CCTV buying alcohol and food in a local shop at 11.15pm but instead of going to his home a few minutes away, he headed to the park.
He had sat on a bench to eat and drink when he was shot around 15 minutes later.
Paramedics were called when he was found but he was pronounced dead at the scene.
Detective Chief Inspector Dave Whellams said investigators hope someone with information who did not go to police at the time might have a “pang of conscience” and come forward with a fresh lead.
He said: “We’ve had this case now for 12 years. It’s been an intense investigation and there are a number of things that we’ve been working on.
“But at the moment we wish to appeal to the public now by the publicity of a reward for £20,000 for information that may provide us with further leads to actually investigate that may lead to the arrest and apprehension of the suspect for Errol’s murder.”
Despite the time that has lapsed, Mr Whellams said there was “always hope”.
He said: “Everybody that’s involved in this murder has to be satisfied that nobody else will come forward and tell the police anything.”
“I, on the other hand, think that allegiances change, loyalties change, and it is quite feasible, quite possible, that someone will have a pang of conscience and will actually come forward and give us that piece of information that points us in a different direction and we can satisfactorily conclude this case,” he added.