The family say the Bangkok firm charged the money for five return plane tickets between the Netherlands and Phuket, and for a hotel booking in Phuket for the five members of their family, amounting to around B240,000.
But the travel company never sent the tickets nor booked the hotel, and it has since been impossible to contact the company, they say.
After buying new tickets, the family have arrived in Phuket with only B50,000 left between them.
On Friday, the family – Peter Neberd and his wife Jiraporn Pajobchan, their son, and Mr Neberd’s parents – visited Phuket's tour guide registration office to get help with a claim against the travel company.
Prapan Kanpraseng, head of the Consumer Protection Department in Phuket, said he would he present the case to Phuket's Governor, Maitree Intusut.
He called on the company involved to respond to the case, which might otherwise damage Phuket's reputation with foreign tourists.