Hesperbot spreads through phishing emails, according to ESET officials.
Like other well-known pieces of malware, it has key logging and screen capture capabilities, and is used to capture online banking credentials.
Hesperbot also tries to trick users into installing malware on their Android, BlackBerry or Symbian phones.
While Hesperbot first appeared last September and a version targeting Australia was discovered in November, activity has doubled in recent weeks, ESET officials warned.
It is now the eighth most prevalent piece of malware in Australia according to ESET's figures, and Australia is the third most affected country behind Turkey and the Czech Republic.
Australian banks known to be targeted by Hesperbot include Commonwealth, MyState, NAB, St George, and Westpac.
Hesperbot also includes code designed to steal Bitcoin wallets.