After graduating from the Turkish High School in Nicosia, Küçük went on to study medicine at the Universities of Istanbul, Lausanne and Paris.

In 1943, he became one of the founders of the Kıbrıs Adası Türk Azınlığı Kurumu (Association of the Turkish Minority of the Island of Cyprus – known as KATAK).

Due to disagreements with some of its members, Küçük parted with KATAK and established the Kıbrıs Millî Türk Halk Partisi (Cyprus National Turkish People's Party – known as KMTHP).

During the 1959 London and Zurich Conferences for the creation of an independent Republic of Cyprus, Küçük represented the Turkish Cypriot community and was able to secure constitutional safeguards for the people.

Küçük died in a Westminster hospital on 15 January 1984, less than a year after the Unilateral declaration of Independence of the Turkish Republic of Northern Cyprus.