Vietnam Airlines has uncovered 20 cases so far this year, and budget carrier Vietjet Air, 11.
Most cases occur on the Hong Kong and mainland China sectors, a Vietjet spokesperson said.
A Vietnam Airlines spokespers said they were done mainly by Chinese passengers, according to a report by the Ministry of Transport.
To Tu Hung, deputy head of the Civil Aviation Authority of Vietnam’s aviation security department, said in the past this was a problem that mainly plagued other carriers, but since late 2016 Vietnamese airlines have also been targeted.
Cash is the main target of the thieves, and is usually stolen early in the morning or late at night when passengers are sleeping.
Following the most recent incident, security officials at Hanoi’s Noi Bai International Airport handed over a 34-year-old Chinese man identified as Hu Dong Huang to the police after he was caught stealing 40,000 yen ($377) from a fellow passenger on a domestic flight from Da Nang to Ha Noi.
There were two cases of theft and an attempted theft on Vietnam Airlines flights in May, all by Chinese nationals.
Vietnamese carriers have been adopting tougher measures to prevent the thefts, including tightening security and training staff to be more alert to the problem.
A number of Chinese nationals have been caught for stealing on flights in Vietnam in recent years, but only two of them were brought to trial and given three to eight years in jail.
Vietnamese law treats theft as a criminal offense only if the stolen property exceeds VND2 million ($87) in value and many Chinese culprits caught in recent years have just been fined and deported, because the stolen assets were valued less than the threshold.
Those rummaging others’ luggage without the cabin crew catching them red-handed and seizing evidence get away without tough action being taken against them.
Nguyen Minh Tuan, deputy director of the Southern Airports Authority, said that thieves could watch people during check-in to see who is carrying valuable belongings.
Once passengers board, the thieves could deliberately put their own luggage nearby and wait for an opportunity, he said.
Tuan said many thieves, even if caught, simply deny the charges, saying they had mistaken someone else’s bag for their own.
"The Civil Aviation Authority of Vietnam (CAAV) should consider slapping a flight ban on thieves caught stealing on flights," a spokesperson for a carrier who asked to remain anonymous told Giao Thong newspaper.
Hung of CAAV said the general impression of airports and airplanes being safe places leaves many Vietnamese passengers vulnerable to theft. The lack of surveillance cameras on planes also makes it difficult to catch thieves in action, he said.
"I'm concerned that many Vietnamese passengers are quite careless with large sums of money and fail to keep an eye on their belongings."