The lawsuit accuses Jean Kasem of elder abuse and inflicting emotional distress on Kasem's children by restricting their access to him before his death, according to the AP news agency.
Kasem was known as host of the American Top 40 radio show and as the voice of Shaggy in the TV animation Scooby Doo.
He died last June at the age of 82.
He had been suffering from dementia, and the battle between his children from a previous marriage and their stepmother Jean began before his death.
They claim she abused him before he died, moved him from Santa Monica to Washington without telling them and, after his death, had him buried in an unmarked grave in Norway despite his wishes to be laid to rest in Los Angeles.
"What she did to my father is reprehensible," daughter Kerri Kasem said, according to AP. "It's disgusting. It's horrific."
Jean Kasem's lawyer H Michael Soroy did not immediately return a request for comment to the news agency.
Kerri Kasem said the family members were taking legal action after US prosecutors decided not to bring criminal charges against Jean Kasem, who was married to the star for more than 30 years.
In May, Los Angeles prosecutors said they could not prove at trial that her actions led to his death.
Kerri has taken out the lawsuit with siblings Julie and Michael Kasem and their uncle Mouner. They are seeking damages of $250,000 (Â£166,000).
But Kerri Kasem said: "We would rather see her in jail than receive one dime. We don't care about the money. We care about justice."
Casey Kasem began his career in the 1950s and found fame with the chart programme in the 1970s.
He famously ended his broadcasts with his signature sign-off: "Keep your feet on the ground and keep reaching for the stars."

The man, named by state media as Ji Zhongxing, 34, from central Shandong province, was injured and taken to hospital.
No-one else was hurt in the blast, which filled part of the Terminal 3 arrivals hall with smoke.
An online microblog attributed to the man says the explosion was to protest at his ill-treatment by Chinese police.
The blog suggests his lower body was paralyzed after he was alleged to have been heavily beaten by security agents in southern China in 2005.
Mr Ji, who is alleged to have been operating an unlicensed motorbike taxi service, was also apparently dissatisfied with the way his complaints against the authorities had been dealt with.
State news agency Xinhua said he detonated the device - a package of gunpowder taken from fireworks - after being prevented from distributing leaflets.
Photos posted on China's Weibo microblogging site showed a dark-haired man waving a white package in the air before the explosion.
Later images from the airport showed the wheelchair on its side with officials treating him on the floor.
Smoke drifted through the terminal after the blast, which occurred shortly before 18:30 (10:30 GMT) near one of the arrival gates.
Xinhua showed several medical workers providing emergency treatment, with police officers also at the scene.
Officials say order has been restored at the airport and there is no disruption to flights.

A woman in her 20s was pushed to the ground and assaulted by a man on a bike on Boundary Road near Bournemouth University's Talbot campus on Thursday.
Dorset Police said they believe it could be linked to two attempted sexual assaults on women in September.
Thursday's attacker is described as white and in his late 20s or early 30s.
Officers said he was approximately 5ft 7in (1.7m), of slight to medium build with short dark hair and wearing a black thigh-length coat and dark trousers.
The victim was walking down a footpath at about 21:40 GMT when the cyclist approached and then assaulted her.
The attacker was riding a dark-coloured mountain bike with silver handle bars and rode off towards Columbia Road after the assault.
Det Ch Insp Sarah Derbyshire said it could be linked to the attempted assaults of women on 13 and 14 September at Boundary Road and Slades Farm.
She is appealing for witnesses.
Three of US DJ Casey Kasem's children and his brother have sued the late star's widow for wrongful death in the latest move in a bitter family feud.
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A man in a wheelchair with an apparent grievance has detonated a small device at Beijing International Airport.
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A sex attack on woman near a university campus could be linked to two other attempted assaults, investigators have said.