There is no direct connection from Zagreb to Rab. However, you can take the bus to Rijeka, take the walk to Rijeka, then take the ferry to Rab. Alternatively, Autotrans operates a vehicle from Zagreb to Rab twice daily. Tickets cost $17 - $40 and the journey takes 5 h 37 min. Autobusni Promet also services this route once daily.
From Zagreb bus to Rijeka, walk to Rijeka, then ferry to Rab. 5 h 5 min 167 kn. From Zagreb bus and ferry to Rab. 5 h 37 min 223 kn. From Zagreb bus to Stinica then car ferry to Rab. 6 h 6 min 212 kn. From Zagreb train to Rijeka, walk to Rijeka, then ferry to Rab. 6 h 49 min 182 kn. From Zagreb drive to Stinica then car ferry to Rab. 3 h 9 min 203 kn.