A family of four faces deportation from Australian after incorrectly filling out a visa application form.

Nina Christidi and Stefanos Stefanoglou have lived in Melbourne with their two children for five years since arriving in the country from Greece.

Christidi said that when she was filling out an online visa application she mistakenly answered "no" to a question asking whether she, or anyone in the family, was planning to study in Australia, believing the question only applied to her.

"It was an honest mistake, I genuinely thought the question referred to whether I intended to study or not," Christidi told News Limited in comments published on Monday.

However, since the couples' children attend school in Melbourne, the Department of Immigration has said that it was provided with misleading information, which is grounds for canceling a visa.

If the family, who live in Oakleigh in Melbourne's southeast, withdraw the incorrect application they face the prospect of their visa being canceled and would have to spend up to US$7,500 to resubmit the paperwork.

"I can't afford to spend the money on another application ... I just wanted to fix my mistake," Christidi said.

"My children have never been to school in Greece. Melbourne is our home."

The children were 11 months and 4 years old when the family moved to Melbourne in 2012.

Christidi's son, Erotokriti, has the condition known as Global Developmental Delay and attends a special school to help and guide him until he is ready for mainstream school.

Christidi said: "He wouldn't stand a chance in Athens."

Christidi added that the prospect of having to leave Australia "worried her sick."

"Australia is our home, we came here to give our children a better life and more opportunities," she said.

"My husband and I work very hard and want to give back to this beautiful country."