The rap campaignatriement was later condemned by some as "the state kidnapp ing ".
Five people who participated and then escaped from the North demanded 100 million yen ($ 880,000; £ 640,000) each.
They don't expect Mr Kim to show up or pay, but hopefully a decision can help in future negotiations.
Thousands of Koreans moved to Japan - many against their will - during its colonial rule of the Korean Peninsula from 1910 to 1945. The vast majority of those involved in the resettlement program were ethnic Koreans who were sold a vision of the "homeland " as a "paradise " - and Japanese brides accompanied them.
North Korea and Japan supported the campaign.
The North was desperate to rebuild itself after being ravaged by World War II and the Korean War.
Japan consideredKoreans as foreigners and was happy to help them resettle.
The combination of discrimination in Japan and North Korean propaganda promising an idyllic life of free health care, education and jobs in the country was a huge temptation.
For many, the reality was forced manual labor on farms, mines or factories, violation of human rights and an inability to leave.
The court case is symbolic - the five plaintiffs accept it.
Image source, Image caption, The North needed manpower after the devastation of the Korean War
The four ethnic Koreans, and the Japanese wife of a Korean who joined the program, all subsequently returned to Japan.
The plaintiffs' attorney, Kenji Fukuda, said: "We don't expect North Korea to accept a ruling or pay damages.
But if they win "we hope the Japanese government can negotiate with North Korea ".
The countries do not have diplomatic relations formelles.
Mr. Kim is named because he is the current leader of the North.
The lawsuit claims that the North plaintiffs deceived the plaintiffs by "fake to move to North Korea, " where "the enjoyment of human rights was generally impossible ".
One of the plaintiffs, ethnic Korean Eiko Kawasaki, 79, told the Associated Press that none would have gone if he had known what to expect. She fled the North in 2003, leaving behind her adult children.
Lee Tae-kyung, who sailed north at age eight in 1960, is another struggling for get compensations.
He told the New York Times: " We were told we were going to a 'Heaven on Earth '. Instead, we were taken to Hell and deprived of a of the most basic human rights: the freedom to leave. "
Mr. Lee fled Koreaof the North after 46 years.