One far-left group has threatened to kill Korkoneas, prompting authorities to send hundreds of police to Amfissa, which is 200km northwest of Athens.
Special forces officers were deployed inside the court itself.
About 800 protesters, most of whom arrived by bus from other parts of Greece, held a peaceful demonstration outside the court, closely monitored by riot police.
They chanted slogans against the police, and held banners reading "The state is the guilty party," and "Convict the murderers and the policies that armed them".
Later, minor clashes broke out when police fired tear gas at a group of about 200 mostly anarchist protesters who marched from the court to a prison complex just outside Amfissa.
Greece's supreme court has rejected bids by the teenager's family to move the trial back to the capital.
The court was told on Wednesday that Gina Tsalikian, Grigoropoulos's mother, was also unable to attend the trial opening as her own mother is in grave condition in an Athens hospital.
Tsalikian, who has also appealed to George Papandreou, the Greek prime minister, argues that holding the trial so far from Athens hampers the presence of key witnesses.
"We do not understand why this trial has to be held in Amfissa," said Alexandros Katsantonisone, one of the Grigoropoulos family's lawyers, outside the court.
Several banks and shops in Amfissa, a town of 12,000 inhabitants, had boarded their storefronts for fear of violence.
Korkoneas has said that in the December incident he fired in the air to disperse youths, including Grigoropoulos, who threw stones at his police car.
An autopsy report indicated that the boy was hit by a bullet that ricocheted onto him. But lawyers for the Grigoropoulos family point to the testimony of witnesses who say the policeman took aim and fired.