Another 162 people were injured, the official Xinhua news agency added. It said the attack had taken place late on Saturday evening.
"It was an organised, premeditated violent terrorist attack," Xinhua said.
Police shot dead five of the attackers and were searching for around five others, it added.
Kunming resident Yang Haifei told Xinhua that he was buying a ticket when he saw a group of people, mostly wearing black, rush into the station and start attacking bystanders.
"I saw a person come straight at me with a long knife and I ran away with everyone," he said. Those who were slower were caught by the attackers. "They just fell on the ground."
Graphic pictures on the Twitter-like microblogging service Sina Weibo showed bodies covered in blood lying on the ground at the station.
There was no immediate word on who was responsible.
State television's microblog said domestic security chief Meng Jianzhu was on his way to the scene.
Weibo users took to the service to describe details of what happened, though many of those posts were quickly deleted by government censors, especially those that described the attackers, two of whom were identified by some as women.
Others condemned the attack.
"No matter who, for whatever reason, or of what race, chose somewhere so crowded as a train station, and made innocent people their target - they are evil and they should go to hell," wrote one user.
The attack comes at a particularly sensitive time as China gears up for the annual meeting of parliament, which opens in Beijing on Wednesday and is normally accompanied by a tightening of security across the country.
China has blamed similar incidents in the past on Islamist extremists operating in the restive far western region of Xinjiang, though such attacks have generally been limited to Xinjiang itself.
China says its first major suicide attack, in Beijing's Tiananmen Square in October, involved militants from Xinjiang, home to the Muslim Uighur people, many of whom chafe at Chinese restrictions on their culture and religion.
Hu Xijin, editor of the influential Global Times newspaper, published by the ruling Communist Party's official People's Daily, wrote on his Weibo feed that the government should say who it suspected of the attack as soon as possible.
"If it was Xinjiang separatists, it needs to be announced promptly, as hearsay should not be allowed to fill the vacuum," Hu wrote.