There are direct connection to Corfu by ferries from Venice, Bari and Brintisi.
Ferries from Ancona goes to Igoumenitsa and you have to take the local ferry (1,5-2 hours trip) to go to Corfu.
Trip's duration is 23-24 hours from Venice and 12 hours from Ancona to Igoumenitsa plus 2 hours for the local ferry.
Ferries from Bari or Brintisi (about 6 hours trip) are cheaper but it is convenience only to italians, as it's a long road trip from North Europe to Bari/Brintisi.
More info here:
Hope that helps - have a nice vacation!