The police had already opened a criminal investigation before this latest complaint, and barred Jeju Air CEO Kim E-bae from leaving the country, but no one has been indicted over the incident.
One of the relatives, Kim Da-hye, denounced the "lack of progress" in investigations.
"We are filled with deep anger and despair. Having taken this extraordinary measure of filing a criminal complaint, we will not give up and will continue to pursue the truth," Mr Kim said in a statement to the media.
Among the 15 people named in the complaint were government officials, airline officials and airport staff responsible for construction, supervision, facility management and bird control.
The complaint filed on Tuesday raises questions around the circumstances of the crash, including whether air traffic control responded appropriately and whether the reinforcement of a mound at the end of the runway violated regulations.
The aircraft, a Boeing 737-800, took off from the Thai capital of Bangkok on the morning of 29 December, and was flying to Muan in South Korea.
Five minutes after the pilots made contact with Muan International Airport, they reported striking a bird and declared a mayday signal.
The pilots then tried to land from the opposite direction, during which the aircraft belly-landed without its landing gear deployed. It later overran the runway, slammed into a concrete structure and exploded.
Earlier this year, investigators said they found bird feathers in both engines of the jet, but did not conclude the extent to which the bird strike was a contributing factor.
Since the incident, some bereaved families have also been targeted by a torrent of conspiracies and malicious jokes online.
These included suggestions that families were "thrilled" to receive compensation from authorities, or that they were "fake victims". As of March this year, eight people have been apprehended for making such derogatory and defamatory online posts.
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