The cause was unclear and an investigation has been launched, the country’s defence ministry said in a statement.
It added that ten crew members and 247 passengers – mostly soldiers and their relatives – died in the crash.
A number of survivors were being treated at an army hospital, the ministry added.
The jet came down in farmland close to Boufarik airport near Algiers and emergency services have been sent to the crash site.
Black smoke could be seen rising near a motorway in footage broadcast on Algerian television, with a crowd of officials also visible in a field next to the crash site.
The tail fin of a plane could also be seen above olive trees, with smoke and flames billowing from the wreckage.
A row of white body bags could be seen on the ground next to the jet.
The country’s state news agency said the Soviet-designed Il-76 plane was heading to Bechar in the south west of the country when it came down some 20 miles (30km) from Algiers soon after take-off.
Algeria has experienced a number of military and civil air disasters in recent years.
Seventy-seven people died in February 2014 when a military plane carrying army members and their families crashed.
Only one person survived after the C-130 Hercules jet came down in the mountainous Oum El Bouaghi region, with the crash being blamed on bad weather.
More from World
LIVE: US military ‘ready’ with options for Trump
‘Proud’ Serbian war criminal Vojislav Seselj has acquittal overturned
Nerve agent attack: Russian TV crew kicked out of Salisbury hospital after ‘appalling’ stunt
LIVE: Zuckerberg’s own data ‘sold to malicious third parties’
Airlines warned over danger from possible airstrikes on Syria
Twenty killed as Brazil prison breakout attempt sparks gunfight
An Air Algerie passenger flight from Burkina Faso to Algiers crashed in northern Mali in July of the same year, killing all 116 people on board, 54 of them French nationals.
In 2003, another Air Algerie flight crashed on take-off after an engine caught fire. All but one of the 103 people on board died.