It said the Government should prioritise work on a number of issues, including the protection of the environment, separation of church and state, and the right to die.
The convention also wants the Government to focus on the definition of the family and reform of the Seanad and Local Government.
Convention Chairman Tom Arnold said the process had been "innovative and historic".
He said: "Our work may lead to changes in our Constitution, the document which reflects the values and aspirations of our society and defines and guarantees our rights as citizens.
"At all times the work of the convention was guided by the principle of equality of voice, and despite some initial concerns that politicians, with their greater expertise in public speaking would dominate proceedings, the citizen members proved more than capable of holding their own in the discussions."
The Government has already committed to holding referendums on same-sex marriage, lowering the voting age and reducing the age of candidacy for presidential candidates.
The convention was made up of 66 randomly chosen citizens, 33 legislators and Mr Arnold.