|The amendments would extend the president's term in office from five to seven years and create a powerful new first vice-president position|
The amendments would extend the president's term in office from five to seven years, create a powerful new first vice-president position and axe the current age minimum of 35 to stand for president.
Opposition groups staged mass protests ahead of the referendum, denouncing it as Aliyev's bid to extend his family's long grip on power in the oil-rich former Soviet republic.
The Council of Europe's constitutional law experts said the draft modifications of the constitution "would severely upset the balance of power by giving unprecedented powers to the president."
Amnesty International said "the amendments will lead to violations of the right to freedom of association."
"The referendum has been accompanied by arrests and intimidation," the rights group said in a statement.
"Those who have attempted to criticise and campaign against these proposals have faced assaults and harassment by the authorities."
The Central Election Commission said that voter turnout had reached 30.6 percent by noon (0800 GMT).
At polling stations in the capital Baku many voters said they supported the proposed changes to the constitution, crediting Aliyev with ensuring political stability during his tenure.
"I voted in favour of the constitutional changes because they are proposed by our president. I trust him and believe that what he proposes is good for Azerbaijanis," said Lala Khalilova, a 46-year-old school teacher.
But some expressed scepticism about the referendum, saying it only serves Aliyev's political ends.
"There were no debates ahead of the referendum. It's all about extending Aliyev's rule," said shop assistant Usif Asadov, 39.
"I voted against it. In democratic countries, there are no perpetual leaders."
- Rights violations -
Aliyev, 54, has led the country since his father Heydar, a former Communist-era boss, died after a decade in power in 2003.
He last won a landslide election victory in 2013 despite OSCE observers pointing to significant problems with the vote. The next elections will be held in 2018.
He is allowed to stand for an unlimited number of presidential terms after a previous disputed referendum in 2009 scrapped a two-term limit.
If passed, the referendum would introduce a new position of first vice president, who would rule in the president's absence.
That duty is currently held by the prime minister, whose appointment requires the approval of parliament.
The amendments also allow the president to call snap leadership elections at will and easily dissolve parliament.
Azerbaijan, a majority-Muslim but secular country wedged between Iran and Russia on the Caspian Sea, has sought to position itself as a modern European state.
It hosted the Eurovision Song Contest in 2012 and this year hosted Formula One races for the first time in Baku.
But activists have raised concerns over alleged human rights violations, with Human Rights Watch in May criticising the country for "cracking down on human rights activists and critical journalists."
"President Ilham Aliyev is the person most responsible for Azerbaijan's appalling human rights record of the last decade," Freedom House said last week.
Polls opened in the referendum at 8am (0400 GMT and were set to close 12 hours later.