Anyone convicted of displaying the symbols, including the Nazi salute and swastika, could be fined up to $27,500 or face 12 months in prison if parliament approves Julian Leeser's private bill.
Mr Leeser said the ban on Nazi symbols was critical in order to stop any legitimacy being attached to them.
"We must deny these extremists access to such symbols, symbols they used to create fear, spread fear and capture new recruits," he told parliament on Monday.
"Don't think this is not happening here right now, our country is dealing with this today."
The introduction of the legislation to the lower house follows a group of neo-Nazis performing the sieg heil salute outside the Victorian parliament earlier in May, following clashes with police and counter-protesters.
A parliamentary committee has recommended the government act with urgency to implement a ban on Nazi symbols.
However, it rejected a similar private bill in the Senate arguing it was not watertight enough.
Opposition Leader Peter Dutton had called on the government to fast-track laws banning Nazi symbols.
Mr Leeser's bill provides exceptions for swastikas displayed as part of Buddhism, Hinduism, or Jainism faiths where there are religious connections to the symbol.
Exceptions would also be made for showing Nazi symbols as part of journalism, education, scientific or artistic purposes.
The Liberal MP said the bill would make the country safer.
"This bill is a affirmation of Australian values, values that respect the quality of Australians from all races, beliefs and backgrounds," Mr Leeser said.
"This bill will ensure there is no legal ambiguity about Nazi displays, demonstrations and actions."
Laws banning Nazi symbols have been introduced in NSW and Victoria.
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