It is the second time the Chronext store on Piccadilly has been targeted in six months.
Four raiders smashed their way through the windows of the Piccadilly store just before 11:00 GMT before making off on two mopeds.
A Met Police spokesman said the gang "made off from the scene with a quantity of goods".
According to the shop's owners, a security guard had tried to fend off the gang until they "slammed the door with an axe".
It is understood a pedestrian who attempted to stop the raid was nearly hit with the axe.
There are no reported injuries.
Officers from the Flying Squad attended but the robbers had already fled. No arrests have been made.
In August the same store was targeted by a gang of armed moped thieves who were tackled to the ground by police who were lying in wait following a tip off.
The gang, armed with knives and an axe, caused more than Â£100,000 of damage to the shop.
Four Met officers were injured during the raid.
In November, four men were jailed over the raid.
An axe-wielding moped gang robbed a central London luxury watch store in a smash and grab raid.