Fuel Permits are not necessary for travel within Hawaii, since Hawaii is not does not participate in the IFTA. For trucks registered in Hawaii that travel in other states and jurisdictions, you must pay quarterly taxes for each state you travel in that participates in the IFTA.
Permits issued in Hawaii are as follows:
One Way Permit — Permits issued for single trip movements are issued for one, one-way round trip movement of oversized or overweight vehicles and objects. These permits will be valid only for the specific date, time, vehicle, and route that is designated in the permit.
Continuous Operation Permit — Continuous operation permits for the movement of oversize and overweight vehicles may be issued for vehicles as long as:
Source of information: http://www.hawaiitrucktax.info/temporary-permits.html