Naji Al-Ali was fatally shot in the back of his neck as he walked to his office in Knightsbridge on July 22 1987.
The 51-year-old, who worked for Kuwaiti newspaper Al-Qabas, was taken to hospital where he remained in a coma until he died a month later.
Mr Al-Ali's cartoons were often perceived as critical of the regime in Palestine and he had received a number of death threats in the years before his death.
In the moments leading up to Mr Al-Ali's murder, he parked his car on Ixworth Place, walked down into Draycott Avenue and onto Ives Street.
Witnesses reported seeing him being followed by the suspected gunman, who they described as being of Middle-Eastern appearance and aged about 25, with collar-length thick black hair that was wavy at the back.
He was wearing a stonewashed denim jacket and dark trousers, police said.
Witnesses describe seeing the suspect close to Mr Al-Ali, holding a black automatic handgun.
An artist's impression of the gunman drawn shortly after the incident has been updated as part of the murder review, to show what the suspect may look like today.
Commander Dean Haydon, head of the Met's counter terrorism command, said: "The brutal murder of Mr Al-Ali devastated his family and 30 years on they continue to feel the loss.
"We have previously reviewed this case and followed a number of lines of enquiry which have not resulted in us identifying these two men.
"However, a lot can change in 30 years – allegiances shift and people who were not willing to speak at the time of the murder may now be prepared to come forward with crucial information.
"We remain open-minded about the motive for Mr Al-Ali's murder and we believe there are people somewhere who have information that could help us bring those responsible for his murder to justice."
The police has urged anyone with information to call the investigation team on 020 3276 9014.
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