[2] All matters are heard before a single judge, including appeals from the Court of Petty Sessions.

[5] In 1908 Hugh Pollock, a Crown Prosecutor from Sydney, was appointed to hear the trial of J F Young for stealing a copper boiler, a relic of HMS Bounty.

[14] Henry Newberry was convicted of failing to be enrolled to vote in Norfolk Island Council elections.

Eggleston J considered the constitutional history of Norfolk Island, concluding that the Australian Waste Lands Act 1855 (Imp),[15] authorised any form of government, representative or non-representative, and this included placing Norfolk Island under the authority of Australia.

[16] The Norfolk Island Act 1957,[10] was the subject of minor amendments in 1963, which included that more than one judge could be appointed to the Court.

[22] One of the changes introduced in 1979 was that the Court could sit outside of Norfolk Island, empowering the Governor-General to make regulations: "(a) making provision for and in relation to sittings of the Supreme Court in a State or in a Territory other than Norfolk Island for the purpose of hearing and determining a matter, otherwise than in the exercise of its criminal jurisdiction, if a Judge is satisfied that the hearing of the matter outside the Territory is not contrary to the interests of justice..."[23]Under the 1979 Act the jurisdiction, practice and procedure of the Supreme Court shall be as provided under "enactment",[24] a term which includes any "Ordinance continued in force by (the 1979) Act".

The Court deals with matters arising under specific Norfolk Island laws such as Probate and Administration of Deceased estates;[26] serious indictable offences and crimes;[27] Bail on serious offences;[28] and registration of Maintenance Orders made by foreign courts (not Australian Child Support assessments);[29] and exercises federal jurisdiction for those Australian federal laws that are expressed to apply to the Territory of Norfolk Island.

Jurisdiction is unlimited except for matters relating to the Offshore Petroleum and Greenhouse Gas Storage Act 2006.