Commonwealth lawyers will argue that former Speaker Peter Slipper's conviction for dishonestly using taxpayer-funded taxi vouchers to visit wineries should stand.

The appeal hearing will continue in the ACT Supreme Court on Thursday at 10am.

Wendy Abraham QC will outline her submissions before Justice John Burns.

The former Queensland MP has admitted using his government travel entitlements to visit the vineyards outside Canberra on three separate occasions in 2010 but always denied he acted dishonestly.

In September, he was placed on a two-year good behaviour bond, ordered to serve 300 hours community service and repay $954 to the Commonwealth.

Mr Slipper was not present in court for the hearing on Wednesday.

His lawyers argued his conviction should be thrown out because it's not clear what constitutes parliamentary business.

© AAP 2014